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For questions about the study of algebraic structures consisting of a set of elements together with a well-defined binary operation that satisfies three conditions: associativity, identity and invertibility.
2
votes
0
answers
21
views
Seeking errata for Rotman's An Introduction To The Theory of Groups
As the title. I can't seem to find the errata to that book (4th edition) online. But I've seen somewhere people say they got it in printing form when buying the book. Does anyone know where to find it …
2
votes
1
answer
42
views
Projective groups and retraction definitions in Lyndon & Schupp
I'm reading Combinatorial Group Theory (by Lyndon & Schupp) and on p.2 they define a projective group $P$ to be such that, for any groups $G$, $H$ with $\gamma: G\to H$ a surjective map and $\pi: P\to …
5
votes
2
answers
209
views
Is every group the semidirect product of its center and inner automorphism group?
For every group $G$, we have $$G/Z(G)\simeq \operatorname{Inn}(G).$$
I wonder whether the quotient projection has a right inverse. I suspect it doesn’t have one in general. But I can’t find a counter …
1
vote
2
answers
44
views
Question over decomposition of $\mathbb{Z}_{mn}$
If $m<n\in\mathbb{N}$ and $(m,n)=1$, then there is a natural isomorphism $h: \mathbb{Z}_{mn}\to \mathbb{Z}_m \times \mathbb{Z}_n$. But I'm a little confused about what happens when multiplying $m$ on …
8
votes
1
answer
717
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Issue with a "proof" for Maschke's Theorem
I came up with a "proof" for the Maschke's Theorem in the representation theory of finite groups that seems to make sense. But it doesn't use the fact that the group being represented is finite. So I …