Finite unitary ring with minimal non-nilpotent group of units

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

Unitary Units of the Group Algebra F2kQ8

g∈G agg −1 is an antiautomorphism of KG of order 2. An element v of V (KG) satisfying v = v is called unitary. We denote by V∗(KG) the subgroup of V (KG) formed by the unitary elements of KG. Let char(K) be the characteristic of the field K. In [2], A.Bovdi and A. Szákacs construct a basis for V∗(KG) where char(K) > 2. Also A. Bovdi and L. Erdei [1] determine the structure of V∗(F2G) for all gr...

A characteristic condition of finite nilpotent group.

This paper gives a characteristic condition of finite nilpotent group under the assumption that all minimal subgroups of G are well-suited in G.

Unitary units in modular group algebras

Let p be a prime, K a field of characteristic p , G a locally finite p-group, KG the group algebra, and V the group of the units of KG with augmentation 1. The anti-automorphism g 7→ g of G extends linearly to KG ; this extension leaves V setwise invariant, and its restriction to V followed by v 7→ v gives an automorphism of V . The elements of V fixed by this automorphism are called unitary; t...

On Nilpotent ideals in the cohomology ring of a finite group

In this paper we find upper bounds for the nilpotency degree of some ideals in the cohomology ring of a finite group by studying fixed point free actions of the group on suitable spaces. The ideals we study are the kernels of restriction maps to certain collections of proper subgroups. We recover the Quillen-Venkov lemma and the Quillen F-injectivity theorem as corollaries, and discuss some gen...