Gl(2,R) and Sl(2,R) are both infinite groups, though Sl(2,R) is a proper subgroup of Gl(2,R). So is it possible to get such isomorphism
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1Welcome to MathSE! What have you tried so far? – ultralegend5385 Dec 03 '23 at 05:26
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3Their centers are isomorphic to $\mathbb{R}^{\times}$ and ${1,-1}$ respectively. So, they cannot be isomorphic. – Geoffrey Trang Dec 03 '23 at 05:29
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@ultralegend5385, I was thinking of the function, but I couldn't get any such – RITAM SADHUKHAN Dec 03 '23 at 05:31
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This question can be closed for a thousand reasons, but not because it is a duplicate of the question in the above link. If someone were to suggest comparing the commutator subgroups of these groups, it turns out that this question is a duplicate of this and this questions? – kabenyuk Dec 03 '23 at 08:06