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May
19
revised Show that $\alpha: G \rightarrow G ,\alpha(g)=g^2$ isomorphism
added 2 characters in body
May
19
comment Show that $\alpha: G \rightarrow G ,\alpha(g)=g^2$ isomorphism
@ASKASK Yeah, probably. But still - at least write out the word fully!
May
19
comment Show that $\alpha: G \rightarrow G ,\alpha(g)=g^2$ isomorphism
I do not understand your attempt. What is "hom", and why is $G$ this?
May
19
revised Why Aren't “Similar” Matrices Actually the Same?
I used to be called Swlabr, a long time ago.
May
15
comment What does this vector notation really mean?
@vadim123 C'mon, this is a valid question. A similar one might be Is “a+0i” in every way equal to just “a”?.
May
13
revised Proof that elements of a free generating set have infinite order.
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May
12
awarded  Sportsmanship
May
12
revised Quotienting by generators in free groups
added 678 characters in body
May
12
answered Quotienting by generators in free groups
May
11
comment Can a group be non-empty by definition of 'group'?
Every group represents the symmetries of something, $X$ say. The empty set is not the symmetries of anything, because if the object $X$ had no symmetries then that is a symmetry - its group is the trivial group.
May
5
awarded  Yearling
May
1
revised About a relation of non-discernability between (classes of) finitely generated groups.
deleted 204 characters in body
May
1
revised About a relation of non-discernability between (classes of) finitely generated groups.
added 211 characters in body
May
1
revised About a relation of non-discernability between (classes of) finitely generated groups.
added 57 characters in body
May
1
comment About a relation of non-discernability between (classes of) finitely generated groups.
Ah, sorry, of course. My mistake. I'll edit that in.
May
1
revised About a relation of non-discernability between (classes of) finitely generated groups.
added 574 characters in body
May
1
revised About a relation of non-discernability between (classes of) finitely generated groups.
added 574 characters in body
May
1
answered About a relation of non-discernability between (classes of) finitely generated groups.
May
1
comment About a relation of non-discernability between (classes of) finitely generated groups.
I think your question would be more readable if you removed every reference to "isomorphism class". In general, this is assumed so you don't need to point it out (but perhaps keep your first line, so as to satisfy pedants!).
May
1
comment For groups $A,B,C$, if $A\times B$ and $A\times C$ are isomorphic do we have $B$ isomorphic to $C$?
I think, perhaps, we should close this question as a duplicate and @ClémentGuérin you should post your Q2 as a new question, linking back to this one. Serios' answer just addresses Q1, which has been asked and answered many times here, so in the interest of Q2 (which I think is very interesting!) and the other new questions, I believe starting again would be better.