Character Degrees, Class Sizes, and Normal Subgroups of a Certain Class of p-Groups

AFFINE SUBGROUPS OF THE CLASSICAL GROUPS AND THEIR CHARACTER DEGREES

In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

A Certain Class of Character Module Homomorphisms on Normed Algebras

For two normed algebras $A$ and $B$ with the character space   $bigtriangleup(B)neq emptyset$  and a left $B-$module $X,$  a certain class of bounded linear maps from $A$ into $X$ is introduced. We set $CMH_B(A, X)$  as the set of all non-zero $B-$character module homomorphisms from $A$ into $X$. In the case where $bigtriangleup(B)=lbrace varphirbrace$ then $CMH_B(A, X)bigcup lbrace 0rbrace$ is...

CHARACTER DEGREES AND NILPOTENCE CLASS OF FINITE p-GROUPS: AN APPROACH VIA PRO-p GROUPS

Let S be a finite set of powers of p containing 1. It is known that for some choices of S, if P is a finite p-group whose set of character degrees is S, then the nilpotence class of P is bounded by some integer that depends on S, while for some other choices of S such an integer does not exist. The sets of the first type are called class bounding sets. The problem of determining the class bound...

Fixed Point Spaces, Primitive Character Degrees and Conjugacy Class Sizes

Groups with Two Extreme Character Degrees and Their Normal Subgroups

We study the finite groups G for which the set cd(G) of irreducible complex character degrees consists of the two most extreme possible values, that is, 1 and |G : Z(G)|1/2. We are easily reduced to finite p-groups, for which we derive the following group theoretical characterization: they are the p-groups such that |G : Z(G)| is a square and whose only normal subgroups are those containing G′ ...