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 $p^{2f}equiv‎ ‎1,({rm mod},16)$‎.

We give a classification of irreducible characters of finite groups of Lie type of p′-degree, where p is any prime different from the defining characteristic, in terms of local data. More precisely, we give a classification in terms of data related to the normalizer of a suitable Levi subgroup, which in many cases coincides with the normalizer of a Sylow p-subgroup. The McKay conjecture asserts...

We study orbit codes in the field extension $ \mathbb{F}_{q^n} $. First we show that automorphism group of a cyclic code is contained normalizer Singer subgroup if generated by subspace not proper subfield then generalize to orbits under subgroup. In situation some exceptional cases arise and open remain. Finally characterize linear isometries between such codes.

We observe that the von Neumann (for short, W*-)envelope of the quantum algebra of functions on the normalizer of the group SU(1, 1) ∼= SL(2,R) in SL(2,C) via deformation quantization contains the von Neumann algebraic quantum normalizer of SU(1, 1) in the frame work of Waronowicz-Korogodsky. We then use the technique of reduction to the maximal subgroup to compute the K-theory, the periodic cy...

The normalizer NW (WJ) of a standard parabolic subgroup WJ of a finite Coxeter group W splits over the parabolic subgroup with complement NJ consisting of certain minimal length coset representatives of WJ in W . In this note we show that (with the exception of a small number of cases arising from a situation in Coxeter groups of type Dn) the centralizer CW (w) of an element w ∈ W is in a simil...

This work presents a precise connection between Clifford circuits, Shor’s factoring algorithm and several other famous quantum algorithms with exponential quantum speed-ups for solving Abelian hidden subgroup problems. We show that all these different forms of quantum computation belong to a common new restricted model of quantum operations that we call black-box normalizer circuits. To define ...

We construct an example of a torsion free freely indecomposable nitely presented non quasiconvex subgroup H of a word hyperbolic group G such that the limit set of H is not the limit set of a quasiconvex subgroup of G In particular this gives a counterexample to the conjecture of G Swarup that a nitely presented one ended subgroup of a word hyperbolic group is quasiconvex if and only if it has ...

The quantum Fourier transform (QFT) is an important ingredient in various quantum algorithms which achieve superpolynomial speed-ups over classical computers. In this paper we study under which conditions the QFT can be simulated efficiently classically. We introduce a class of quantum circuits, called normalizer circuits: a normalizer circuit over a finite Abelian group is any quantum circuit ...

Abstract We study toric G -solid Fano threefolds that have at most terminal singularities, where is an algebraic subgroup of the normalizer a maximal torus in their automorphism groups. All varieties are assumed to be projective and defined over field complex numbers.

Let (AS , S) be an Artin-Tits and X a subset of S ; denote by AX the subgroup of AS generated by X. When AS is of spherical type, we prove that the normalizer and the commensurator of AX in AS are equal and are the product of AX by the quasi-centralizer of AX in AS . Looking to the associated monoids A + S and A + X , we describe the quasi-centralizer of A+X in A + S thanks to results in Coxete...