Abstract We present a sufficient condition for the $kG$ -Scott module with vertex $P$ to remain indecomposable under Brauer construction any subgroup $Q$ of as $k[Q\,C_G(Q)]$ -module, where $k$ is field characteristic $2$ , and semidihedral -subgroup finite group $G$ . This generalizes results cases abelian or dihedral. The indecomposability defined by R. Kessar, N. Kunugi Mitsuhashi. motivatio...

Let p be an odd prime number and F a field containing a primitive pth root of unity. We prove a new restriction on the group-theoretic structure of the absolute Galois group GF of F . Namely, the third subgroup G (3) F in the descending p-central sequence of GF is the intersection of all open normal subgroups N such that GF /N is 1, Z/p , or the modular group Mp3 of order p .

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 $p^{2f}equiv‎ ‎1,({rm mod},16)$‎.

This paper establishes the first four moment expansions to the order o(a^−1) of S_{t_{a}}^{prime }/sqrt{t_{a}}, where S_{n}^{prime }=sum_{i=1}^{n}Y_{i} is a simple random walk with E(Yi) = 0, and ta is a stopping time given by t_{a}=inf left{ ngeq 1:n+S_{n}+zeta _{n}>aright}‎ where S_{n}=sum_{i=1}^{n}X_{i} is another simple random walk with E(Xi) = 0, and {zeta _{n},ngeq 1} is a sequence of ran...

Let p be an odd prime number, k an imaginary abelian field containing a primitive p-th root of unity, and k∞/k the cyclotomic Zp-extension. Denote by L/k∞ the maximal unramified pro–p abelian extension, and by L′ the maximal intermediate field of L/k∞ in which all prime divisors of k∞ over p split completely. Let N/k∞ (resp. N ′/k∞) be the pro–p abelian extension generated by all p-power roots ...

Abstract. In this article, we consider the group F∞ 1 (N) of modular units on X1(N) that have divisors supported on the cusps lying over∞ of X0(N), called the ∞-cusps. For each positive integer N , we will give an explicit basis for the group F∞ 1 (N). This enables us to compute the group structure of the rational torsion subgroup C∞ 1 (N) of the Jacobian J1(N) of X1(N) generated by the differe...

Flag codes are multishot network consisting of sequences nested subspaces (flags) a vector space Fqn, where q is prime power and Fq, the finite field size q. In this paper we study construction on Fq2k full flag having maximum distance (optimum codes) that can be endowed with an orbital structure provided by action subgroup general linear group. More precisely, starting from subspace code dimen...

The ring Zk(+, .) mod p k with prime power modulus (prime p > 2) is analysed. Its cyclic group Gk of units has order (p − 1)p, and all p-th power n residues form a subgroup Fk with |Fk| = |Gk|/p. The subgroup of order p − 1, the core Ak of Gk, extends Fermat’s Small Theorem (FST ) to mod p, consisting of p − 1 residues with n ≡ n mod p. The concept of carry, e.g. n in FST extension n ≡ np + 1 m...