Answer by Marty Isaacs for Subgroups from which all class functions extend to...
This does not really address the two questions, but here is an example where segregated subgroups arise fairly naturally. Let $A \subseteq {\rm Aut}(G)$, where $|A|$ and $|G|$ are coprime. Let $C =...
View ArticleAnswer by Geoff Robinson for Subgroups from which all class functions extend...
I think that the group ${\rm SL}(2,3)$ shows that the answer to both questions is"no" in general. It has a proper non-Abelian subgroup (quaternion of order $8$) and a non trivial center. Its only...
View ArticleSubgroups from which all class functions extend to class functions on the...
Until someone suggests better terminology, let me call a subgroup H of a finite group G segregated if every class function on H can be extended to a class function on G. Equivalently, H should have the...
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