The affine general linear group acting on a vector space over prime field is well-understood mathematical object. Its elementary abelian regular subgroups have recently drawn attention in applied mathematics thanks to their use cryptography as way hide or detect weaknesses inside block ciphers. This paper focused building convenient representation of elements which suits better the purposes cry...

let $g={rm sl}_2(p^f)$ be a special linear group and $p$ be a sylow‎ ‎$2$-subgroup of $g$‎, ‎where $p$ is a prime and $f$ is a positive‎ ‎integer such that $p^f>3$‎. ‎by $n_g(p)$ we denote the normalizer of‎ ‎$p$ in $g$‎. ‎in this paper‎, ‎we show that $n_g(p)$ is nilpotent (or‎ ‎$2$-nilpotent‎, ‎or supersolvable) if and only if $p^{2f}equiv‎ ‎1,({rm mod},16)$‎.

Abstract Let k be an algebraically closed field of characteristic p > 0 and let G a symplectic or general linear group over . We consider induced modules for under the assumption that is bigger than greatest hook length in partitions involved. give explicit constructions left resolutions by tilting modules. Furthermore, we injective certain truncated categories. show multiplicities indecompo...