Search results for " 20C15"
showing 4 items of 4 documents
The average element order and the number of conjugacy classes of finite groups
2021
Abstract Let o ( G ) be the average order of the elements of G, where G is a finite group. We show that there is no polynomial lower bound for o ( G ) in terms of o ( N ) , where N ⊴ G , even when G is a prime-power order group and N is abelian. This gives a negative answer to a question of A. Jaikin-Zapirain.
Brauer correspondent blocks with one simple module
2019
One of the main problems in representation theory is to understand the exact relationship between Brauer corresponding blocks of finite groups. The case where the local correspondent has a unique simple module seems key. We characterize this situation for the principal p-blocks where p is odd.
Finite 2-groups with odd number of conjugacy classes
2016
In this paper we consider finite 2-groups with odd number of real conjugacy classes. On one hand we show that if $k$ is an odd natural number less than 24, then there are only finitely many finite 2-groups with exactly $k$ real conjugacy classes. On the other hand we construct infinitely many finite 2-groups with exactly 25 real conjugacy classes. Both resuls are proven using pro-$p$ techniques and, in particular, we use the Kneser classification of semi-simple $p$-adic algebraic groups.
p-Blocks relative to a character of a normal subgroup
2018
Abstract Let G be a finite group, let N ◃ G , and let θ ∈ Irr ( N ) be a G-invariant character. We fix a prime p, and we introduce a canonical partition of Irr ( G | θ ) relative to p. We call each member B θ of this partition a θ-block, and to each θ-block B θ we naturally associate a conjugacy class of p-subgroups of G / N , which we call the θ-defect groups of B θ . If N is trivial, then the θ-blocks are the Brauer p-blocks. Using θ-blocks, we can unify the Gluck–Wolf–Navarro–Tiep theorem and Brauer's Height Zero conjecture in a single statement, which, after work of B. Sambale, turns out to be equivalent to the Height Zero conjecture. We also prove that the k ( B ) -conjecture is true i…