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Results tagged with finite-groups
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user 4008
Questions on group theory which concern finite groups.
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
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
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