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We all love normal subgroups, and in searching the web for the answer to my question I've found plenty of resources for ways to indicate normal subgroups. That's not what I'm looking for. When one wants to say $H$ is a subgroup of $G$ (not necessarily a normal subgroup, normal status is unknown), what is the intended symbol for that purpose? Does everyone just use the less-than \lt symbol? One could simply use a backslash symbol for setminus, but I'm betting parsers that automatically read LaTeX for the purposes of moving equations between math softwares probably process \setminus better. In a similar spirit, is there a LaTeX symbol for non-normal subgroup?

Edited for clarification: I am not looking for how to say "not a normal subgroup", that is, I'm not looking for a crossed out normal subgroup symbol, or a "not" symbol in front of a normal subgroup symbol. I'm looking for a standard subgroup symbol that doesn't reference "normalness" in any way.

Travis Bemrose
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  • Woah. And why isn't my LaTeX displaying right in the question? – Travis Bemrose Apr 13 '14 at 03:45
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    Welcome to TeX.SE. This site specifically does not render TeX unlike the math site. Can you post an image of the symbol you are looking for. Also check with detexify to see if you can find the symbol there. – Peter Grill Apr 13 '14 at 03:47
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    BTW, does \not\trianglelefteq produce what you are looking for? That is just a guess, extrapolating from Normal subgroups. – Peter Grill Apr 13 '14 at 03:51
  • @PeterGrill Strange that the TeX site wouldn't render TeX. No, the triangle (a closed less than symbol) is the intrinsic property of any symbol for normal subgroup (including or not including an underline etc, are all ancillary to the left pointing triangle). When handwritten, the plain subgroup symbol is the same as the less-than character < on the comma key on the keyboard. For formatting purposes, \lt is preferred over < in inequalities. Similarly, we use \setminus instead of \ or \backslash. I'm wondering if there's something other than < or \lt for "subgroup". – Travis Bemrose Apr 13 '14 at 04:23
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    Since this is a site to ask questions about TeX code it doesn't make sense to render it. See Why doesn't maths render as maths?. – Peter Grill Apr 13 '14 at 05:09
  • @PeterGrill Hmm, I'd think the desire to show the code alongside the rendering would be useful enough in order to not require the effort cost of generating, uploading, and linking images (as well as the file storage cost). Incidentally, I've favorited that post so I can find the links to TeX-to-image tools referenced there (even though it wouldn't render a simple $\lt$ for me). How can I find favorited questions again later on SE sites? – Travis Bemrose Apr 13 '14 at 05:53
  • @Travis it's worth noting that mathjax is absolutely not LaTeX or TeX, so it isn't a 'rendering'. TeX isn't just for maths :) That said, you might want to ask that particular question on meta when you can (or meta.math?) – Sean Allred Apr 13 '14 at 06:03
  • The question seems to be off-topic, as it is about a proper symbol for subgroup relation rather than displaying a symbol using TeX. According to MathWorld, subgroup relation is expressed using either the less-than character or a subset relation symbol. – Jukka K. Korpela Apr 13 '14 at 06:35
  • I think you can use either of the <, \lt, \le, or even \leqslant symbols. There does not seem to be an overall consensus on whether to write \lt or \le. The best thing to do with this is to define a new macro \newcommand{\subgr}{\lt} (or \le or \leqslant or \eqslantless, ... whatever floats your boat) and use the \subgr macro whenever you need to use the subgroup symbol. Then you can change it easily and hassle-free if need be. – moewe Apr 13 '14 at 06:35
  • Just a note: \lt does seem to be a non-standard command, my LaTeX with amssymb and mathtools didn't know it, but some HTML math renderers seem to use it instead of < so as to not have something that looks like the start of an HTML tag. – moewe Apr 13 '14 at 08:32
  • Check if you find something you like here. – MattAllegro Apr 13 '14 at 10:14
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    My teachers of group theory always used the simple \leq symbol for saying “is a subgroup of” and \unlhd for “is a normal subgroup of”. If you say “is a subgroup of”, you're supposing nothing about normality. – egreg Apr 13 '14 at 10:26
  • @SeanAllred I realize TeX is for typesetting in general and not just for math, but I'm not quite sure what you're getting at. I know they're all different, but I can't explain the difference between TeX and LaTeX, and it seems most people use them interchangeably. I think of LaTeX as some sort of extension of TeX and so TeX:LaTeX:{MathJax, etc.} as C:C++:compilers. Did I misuse the word rendering? In order to see the typesetting, you have to have something render it first right? – Travis Bemrose Apr 13 '14 at 16:13
  • @JukkaK.Korpela How does that distinction make it off topic? The example on MathWorld shows me what it looks like (which I already knew), but doesn't tell me the code used. My question is whether there is a specific TeX/LaTeX code for subgroup (like \setminus when one could just use \backslash or \) or whether everyone just uses \lt, \le, etc. – Travis Bemrose Apr 13 '14 at 16:20
  • Thanks @moewe, MattAllegro, egreg for your input (I'd vote your comments up if I could, but le sigh). It seems there is no special/distinct code/symbol, which explains the negative results of my original search. – Travis Bemrose Apr 13 '14 at 16:33
  • The question which symbol should be used is a matter of conventions of mathematical notations, thus quite independent of TeX. When you have decide which symbol you wish to use (so that you can show an image of it and/or identify it as a coded character), you may have a question about displaying it using some techniques, such as TeX. – Jukka K. Korpela Apr 13 '14 at 16:41
  • I might be horribly wrong, but I think that (the semantically named) \setminus exists because \backslash has a different character class. But there is no point in LaTeX defining all kinds of symbols that boil down to the exactly same character (like < and a possible subgroup symbol might): It is for the user to decide which commands he would like to have and to define them. – moewe Apr 13 '14 at 16:56
  • @JukkaK.Korpela I see. I think my question is subtly different than that. Let me see if I can elucidate. I know the proper (acceptable) math symbol(s) to use, that is not my question. Just as "resume" will work when "résumé" is more proper, I am not asking which "e" should I use, nor am I asking about different fonts. My question would be more equivalent to: knowing that different encodings have different character sets, and knowing that (the original 128 character) ASCII encoding does not have "é", asking the unicode community what (if any) is the unicode codepoint for "é". – Travis Bemrose Apr 13 '14 at 16:56
  • @JukkaK.Korpela The feedback I'm getting seems to indicate the equivalent of: "There are probably extensions of the standard unicode that would have the symbol you're looking for, or you can make your own extension, but there is no known codepoint in the standard unicode that is specifically for what you're looking for." (I realize that in reality, é in unicode is U+00E9.) – Travis Bemrose Apr 13 '14 at 17:02
  • The concept “extensions of the standard unicode” does not make much sense, given what Unicode is, and I don’t see anyone having suggested such things. If you are trying to ask whether there is a character that resembles “<” but specifically denotes subgroup relation, then this is not about TeX at all. It would make perfect sense even if (heaven forbid) TeX did not exist. (And the answer is “no”.) – Jukka K. Korpela Apr 13 '14 at 17:22
  • @Travis Re typesetting: MathJAX uses HTML's DOM, so it isn't TeX. It uses syntax very similar to TeX's, but it isn't the same technology. LaTeX is a set of macros on top of TeX, so TeX is still the actual engine behind it all. MathJAX doesn't use this engine, and is mathematics-specific. A quick search of texdoc symbols-a4 does not reveal any such symbol with group in the name, so I suppose my guess per the actual Q is in line with popular opinion. – Sean Allred Apr 13 '14 at 17:36
  • Yes @JukkaK.Korpela, that is my question. The inequality symbols and the subgroup symbols, while visually indistinct, are inherently different. I was wondering if there was a separate code/character in TeX/LaTeX for the separate symbol, or whether people use the same characters. Please forgive my beginners ignorance, but I don't see how this is not what TeX/LaTeX are about.(?) – Travis Bemrose Apr 13 '14 at 17:37
  • @JukkaK.Korpela Rereading your comment from an hr ago, I see that you already made the distinction between symbol, character (code), and display. My question was not regarding the first, or third, but the second. – Travis Bemrose Apr 13 '14 at 17:51

2 Answers2

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After a bit of searching I found \leqslant, which does the trick.

Martin Schröder
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max
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All input so far seems to indicate that no, there's no default or standard code for subgroup, and people use some version of the inequality symbols: <, \le, etc.

Travis Bemrose
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    People use different symbols. And “<” is not an “inequality symbol”, it is LESS-THAN SIGN (though it can be used to denote things other than the common arithmetic relation). – Jukka K. Korpela Apr 13 '14 at 16:43
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    In any case, you should define such a symbol: \newcommand\subgroup{\lw} or \newcommand\normsubgroup{\leq}. – Sean Allred Apr 13 '14 at 17:26
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    @JukkaK.Korpela I realize people define different platonic symbols for whatever context they're working in, and independently use various computer characters to represent those symbols, and independently display those characters in various fonts. Saying that the screen is displaying a character instead of a symbol is pointless. My statement was that since there does not seem to be any character specifically for the subgroup symbol, people use the same characters as they use for the inequality symbols. – Travis Bemrose Apr 13 '14 at 17:31
  • @JukkaK.Korpela I'd agree that making the distinction doesn't really add to the conversation; the result is the same. – Sean Allred Apr 13 '14 at 17:37
  • Tact: pointless -> moot – Travis Bemrose Apr 13 '14 at 17:45
  • @Travis 'moot' has different meanings on different sides of the Atlantic. Is your sense east or west? – cfr Apr 13 '14 at 19:12
  • @cfr Oh? I'm American, so west. When I was rereading the conversation(s) to ensure I understood everything presented, I saw that my original verbiage could be interpreted as emotionally charged, so I was simply looking for a similar word without the emotional connotation. – Travis Bemrose Apr 13 '14 at 20:45
  • @cfr Different meaning indeed. I see how that would change the connotation of my statement. Although, I disagree with Oxford Dictionary's claim that in North America, use of the word moot has anything to do with uncertainty. It has more to do with meaningless, or absence of a difference. In fact, when I wrote that, the phrase "a distinction without a difference" was in my head. – Travis Bemrose Apr 13 '14 at 20:54
  • @Travis I only discovered this recently when a colleague queried my use of 'moot point'. I, apparently, picked this up while living in the States and had no idea that it had a different meaning in my native dialect. (The complexities of global living!) – cfr Apr 13 '14 at 21:09
  • @SeanAllred Defining a new command would defeat the purpose of using a standard one that multiple apps would recognize. – Travis Bemrose Feb 20 '22 at 19:55