Fixed point spaces, primitive character degrees and conjugacy class sizes

Fixed Point Spaces, Primitive Character Degrees and Conjugacy Class Sizes

Products of Conjugacy Classes and Fixed Point Spaces

Note that the hypothesis that V has no two-dimensional composition factors is vacuous if the characteristic of k is not 2. For our intended subsequent application it is critical that the g ∈ G that we choose does not depend on V . We also prove a variant of the previous corollary for direct products of finite simple groups. If V is a G-module, let CV (g) denote the fixed space for g ∈ G. We use...

Fixed Point Theorems on Complete Quasi Metric Spaces Via C-class and A-Class Functions

In this paper, we present some fixed point theorems for single valued mappings on $K$-complete, $M$-complete and Symth complete quasi metric spaces. Here, for contractive condition, we consider some altering distance functions together with functions belonging to $C$-class and $A$-class. At the same time, we will consider two different type $M$ functions in contractive conditions because the qu...

Transversal spaces and common fixed point Theorem

In this paper we formulate and prove some xed and common xed pointTheorems for self-mappings dened on complete lower Transversal functionalprobabilistic spaces.

p-divisibility of conjugacy class sizes and normal p-complements

LetN be a normal subgroup of a groupG and let p be a prime. We prove that if the p-part of jx j is a constant for every prime-power order element x 2 N n Z.N /, then N is solvable and has normal p-complement.