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Results tagged with finite-groups
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user 4008
Questions on group theory which concern finite groups.
1
vote
A condition on finite groups
Such automorphisms appear naturally when one tries to analyse the group of automorphisms of $G$ preserving $H$ ($H$ may for instance be a characteristic subgroup so that it is preserved by all automor …
- 22.6k
34
votes
Accepted
Which groups have only real and quaternionic irreducible representations?
An irreducible representation is real or quaternionic precisely when its
character is real-valued. By the Peter-Weyl theorem all characters are
real-valued precisely when every element in the group is …
- 22.6k
21
votes
Orbit structures of conjugacy class set and irreducible representation set under automorphis...
I think that an example of non-equivalent permutation sets is given by
$G=(\mathbb Z/p\mathbb Z)^n$ for $n>2$ (and $p$ a prime). Then the automorphism
group is $\mathrm{GL}_n(\mathbb Z/p\mathbb Z)$, t …
- 22.6k