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Results tagged with gr.group-theory
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user 1593
Questions about the branch of algebra that deals with groups.
29
votes
Accepted
Is there a non-trivial group G isomorphic to Aut(G)?
The automorphism group of the symmetric group $S_n$ is (isomorphic to) $S_n$ when $n$ is different from $2$ or $6$. In fact, if $G$ is a complete group you can ascertain that $G \simeq \mathrm{Aut}(G) …
- 8,842
20
votes
How can I have a copy of this old paper by Frobenius?
It is freely available online. You can find it here:
http://goo.gl/pDkRi6
(Download the file and take a look at pages 455-459 of it.)
- 8,842
16
votes
The set of orders of elements in a group
For every fixed $n \in \mathbb{N}$, Rolf Brandl and Shi Wujie gave in Finite groups whose element orders are consecutive integers (Journal of Algebra, 143, 388-400 (1991).) a complete classification o …
- 8,842
8
votes
1
answer
3k
views
On order of subgroups in abelian groups
I wonder whether any of you guys has already read the homonymous note by R. Beals in the December 2009 issue of the Monthly.
If so, would you be so kind as to let me know about the main ideas in Beal …
- 8,842
27
votes
1
answer
3k
views
An anecdote by R. Schmidt
Did anybody here ever read those lines by R. Schmidt (?) where he talked about the terseness of articles in group theory in the days prior to the conclusion of the classification of the finite simple …
7
votes
Origin of group theory problem (bound on number of Sylow subgroups)
I consider that it is not at all inappropriate to inform you that a solution to this problem was showcased in the May 2017 issue of the Monthly.
If I understand correctly, the editors of the problem …
- 8,842