New answers tagged infinite-groups
8
votes
Accepted
An example of an infinite group $G$ such that $\operatorname{Aut}(G)\cong$ $\operatorname{Sym}(G)$.
Let $X$ be an infinite set, and let $G=\operatorname{FSym}(X)$, the group of finitary permutations of $X$ (i.e., permutations that fix all but finitely many elements of $X$).
Then $\operatorname{Aut}(...
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1
vote
Accepted
Extension problem on one-dimension representation on Abelian groups
The condition that every map from a subgroup $\alpha: H \to C$ can be extended to a map $\alpha': G \to C$ is true if and only if $C$ is a divisible group. In particular, it's true when $C$ is the ...
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