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Results tagged with gr.group-theory
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user 6574
Questions about the branch of algebra that deals with groups.
10
votes
Accepted
How to find more (finite almost simple) groups with a given Sylow subgroup
If you are only interested in actions on the Sylow p-subgroup, you may not need to find all groups, but just all so-called p-fusion patterns, as formalized in the theory of fusion systems due to Puig, …
- 2,246
6
votes
When are all centralizers in a Lie group connected?
Centralizers of various types of subgroups, and their relationship to invariants like the cohomology of the classifying space $BG$ has a long history of study, at least going back to the papers from t …
- 2,246
33
votes
Accepted
Why are Schur multipliers of finite simple groups so small?
The Schur multiplier $H^2(G;{\mathbb C}^\times) \cong H^3(G;{\mathbb Z})$ of a finite group is a product of its $p$-primary parts
$$H^3(G;{\mathbb Z}) = \oplus_{ p | |G|} H^3(G;{\mathbb Z}_{(p)})$$
…
- 2,246
20
votes
Accepted
Definition of "finite group of Lie type"?
I feel a bit funny posting this as an answer to someone who has written a book with "finite groups of Lie type" in the title.
But I also find the matter both confusing and interesting (and full of co …
- 2,246