Questions tagged [cfsg-free]
Use this tag for the request of a proof free of use of the classification of the finite simple groups.
6
questions
6
votes
1
answer
529
views
If G is an almost simple group, then Aut(G) is complete?
If G is an almost simple group, then Aut(G) is complete?
Apologies - I meant to post this on Stack Exchange
Just wondering if anyone has a reference to the above - it's quoted on Wikipedia (so ...
- 63
6
votes
0
answers
297
views
(CFSG-free) Finite simple groups whose character degrees square divide its order
Let $G$ be a finite group. It is well-known that for all irreducible complex character $\chi$ then $\deg(\chi)$ divides $\lvert G\rvert$. Motivated by some problems with modular tensor categories, we ...
- 25.2k
4
votes
2
answers
353
views
Outer automorphism of a finite simple group which is isomorphic to a subgroup of $S_p$
Here is a statement having a proof that involved the CFSG.
Let $p$ be a prime, and $S$ be a nonabelian finite simple group such that $S$ is isomorphic to a subgroup of $S_p$ with $p\mid |S|$. Then $\...
- 385
7
votes
1
answer
328
views
CFSG-free bound for the number of generators of a finite simple group
We know that every finite simple group can be generated by $2$ elements.
This (correct me if I'm wrong) was proved, as far as I know, by Steinberg (Steinberg, R. (1962). Generators for Simple Groups. ...
- 731
40
votes
6
answers
5k
views
What are some interesting corollaries of the classification of finite simple groups?
The classification of finite simple groups, whether it be viewed as finished, or as a work in progress, is (or will be) without doubt an enormous achievement. It clearly sheds a great deal of light on ...
26
votes
3
answers
2k
views
Highly transitive groups (without assuming the classification of finite simple groups)
What is known about the classification of n-transitive group actions for n large without using the classification of finite simple groups? With the classification of finite simple groups a complete ...
- 27.6k