Which group is simple?

Asked Jan 16 '21 at 14:44

Active Jan 16 '21 at 14:49

Viewed 19 times

I am currently looking whether a group G of the following order is simple or not

$ord(G)=100$
$ord(G')=200$

We have first that for $G$, $ord(G)=2^25^2$. For $G'$ we have that $ord(G')=2^35^2$. Now with the third theorem of Sylow we have, that in both case there is only one $5-$Sylowgroup. But why $G$ is not simple, while $G'$ is simple? I just try to follow the thinking of this site Click here

edited Jan 16 '21 at 14:49

asked Jan 16 '21 at 14:44

Frederick Manfred

"while $G'$ is simple? " Why do you think so? This is not true. – Dietrich Burde Jan 16 '21 at 14:47
I suppose you have read the solution here. There is a typo. It should say "Hence $G$ is not a simple group (because it says "Thus the group $G$ has a unique proper normal $5$-Sylow subgroup of order $25$.") – Dietrich Burde Jan 16 '21 at 14:49
Yeah sorry maybe I am just tired but the group of 200 is on this site simple and the group of 100 not. Why? They have both one $5-$ Sylowgroup... – Frederick Manfred Jan 16 '21 at 14:51
@DietrichBurde ahhh now everything is clear... I got confused exactly because of this! – Frederick Manfred Jan 16 '21 at 14:51
Yes, exactly....you need to read also the argument before. – Dietrich Burde Jan 16 '21 at 14:52

Which group is simple?

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