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Results tagged with finite-groups
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user 2805
Questions on group theory which concern finite groups.
7
votes
1
answer
4k
views
Subgroups of direct product of groups
I am interested in the following question on products of finite groups. Let $\Gamma$ be a subgroup of $U_1\times U_2$ such that the compositions with the canonical projections $\Gamma \subset U_1\time …
- 887
5
votes
1
answer
323
views
Product of all conjugacy classes
Related to this post of my coauthor Sebastien, I should also mention that one can also prove the following dual result:
For any finite group G, the following identity holds:
$$
\left(\prod_{j=0}^m \fr …
- 887
5
votes
Product of all conjugacy classes
At Geoff's suggestion I have found that the identity for the product of all conjugacy classes is attributed to Harada and it can be found for example Corollary 4.15 in the book "Character Theory and t …
- 887
9
votes
3
answers
3k
views
Faithful characters of finite groups
Related to a previous question I am asking furthermore a proof
for the following:
Question 1: If $\chi$ is a faithful irreducible character of a
finite group $G$ then the regular character of $G$ is …
- 887
17
votes
5
answers
3k
views
Reference for this theorem in representation theory?
Let $G$ be a finite group and $\chi$ be an irreducible character of
$G$ (characteristic zero algebraically closed base field). If $H$ is
the kernel of $\chi$ then the irreducible representations of $G …
- 887