Mathematical Proceedings of the Cambridge Philosophical Society Page 1 Mathematical
Proceedings of the Cambridge Philosophical Society VOL. 176 JANUARY 2024 PART 1 …

In this paper we study the realizability question for commuting graphs of finite groups: Given
an undirected graph $ X $ is it the commuting graph of a group $ G $? And if so, to …

For an element $ x $ of a finite group $ T $, the $\mathrm {Aut}(T) $-class of $ x $ is the set
$\{x^\sigma\mid\sigma\in\mathrm {Aut}(T)\} $. We prove that the order $| T| $ of a finite …

Problem 21 of Brauer's list of problems from 1963 asks whether for any positive integer $ k $
there are finitely many isomorphism classes of groups that occur as the defect group of a …

Let G be a finite group of order divisible by a prime p. The number of conjugacy classes of p-
elements and p-regular elements of G is at least 2 p− 1. Also, the number of p-rational and …

Let G be a finite group and P a Sylow 2-subgroup of G. We obtain both asymptotic and
explicit bounds for the number of odd-degree irreducible complex representations of G in …

Let $ p $ be a prime. We construct a function $ f $ on the natural numbers such that $ f
(x)\to\infty $ as $ x\to\infty $ and $ k_ {p}(G)+ k_ {p'}(G)\geq f (| G|) $ for all finite groups $ G …

Motivated by a 2004 conjecture by the author and J. Sangroniz, Y. Yang has recently proved
that if G is solvable then the index in G of the 8th term of the ascending Fitting series is …

The exterior degree d∧(G) of a finite group G is the probability that a pair (x, y) of elements
x, y chosen uniformly at random in G satisfies x∧ y= 1∧, where∧ is the operator of …

Full article: Bounds on the largest Kronecker and induced multiplicities of finite groups Skip to
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