On the basis of an initial interest in symmetric cryptography, present work we study a chain subgroups. Starting from Sylow $2$-subgroup AGL(2,n), each term is defined as normalizer previous one group on $2^n$ letters. Partial results and computational experiments lead us to conjecture that, for large values $n$, index consecutive does not depend $n$. Indeed, there strong evidence that sequence...

Let α be a coprime automorphism of group G prime order and let P an α-invariant Sylow p-subgroup G. Assume that p∉π(CG(α)). Firstly, we prove is p-nilpotent if only CNG(P)(α) centralizes P. In the case Sz(2r) PSL(2,2r)-free where r=|α|, show p-closed CG(α) normalizes As consequence these two results, obtain G≅P×H for H We also generalization Frobenius p-nilpotency theorem groups admitting autom...

In 1979, Miller proved that for a group $G$ of odd order, two minimal codes in $\mathbb{F}_2G$ are $G$-equivalent if and only they have identical weight distribution. 2014, Ferraz-Guerreiro-Polcino Milies disprove Miller's result by giving an example non-$G$-equivalent with this paper, we give characterization finite abelian groups so over specific set codes, equality important parameters impli...

Classifying endotrivial kG-modules, i.e., elements of the Picard group stable module category for an arbitrary finite G, has been a long-running quest. By deep work Dade, Alperin, Carlson, Thevenaz, and others, it reduced to understanding subgroup consisting modular representations that split as trivial k direct sum projective when restricted Sylow p-subgroup. In this paper we identify first co...

It is known that the Sylow subgroups of a Frobenius complement are cyclic or generalized quaternion. In this paper it is shown that there are no restrictions at all on the structure of the Sylow subgroups of the FrobeniusWielandt complements that appear in the well-known Wielandt's generalization of Frobenius' Theorem. Some examples of explicit constructions are also given. 0. Introduction Let ...