Nonsolvable Groups All of Whose Character Degrees are Odd-Square-Free

Nonsolvable Groups All of Whose Character Degrees Are Odd-Square-Free

A finite group G is odd-square-free if no irreducible complex character of G has degree divisible by the square of an odd prime. We determine all odd-square-free groups G satisfying S 6 G 6 Aut(S) for a finite simple group S. More generally, we show that ifG is any nonsolvable odd-square-free group, then G has at most two nonabelian chief factors and these must be simple odd-square-free groups....

Nonsolvable Finite Groups All of Whose Local Subgroups Are Solvable

TABLE OF CONTENTS

Nonsolvable groups with few character degrees

Finite groups all of whose proper centralizers are cyclic

‎A finite group $G$ is called a $CC$-group ($Gin CC$) if the centralizer of each noncentral element of $G$ is cyclic‎. ‎In this article we determine all finite $CC$-groups.

Nonsolvable Groups with No Prime Dividing Three Character Degrees

Throughout this note, G will be a finite group, Irr(G) will be the set of irreducible characters of G, and cd(G) will be the set of character degrees of G. We consider groups where no prime divides at least three degrees in cd(G). Benjamin studied this question for solvable groups in [1]. She proved that solvable groups with this property satisfy |cd(G)| 6 6. She also presented examples to show...