Abstract Let G be a simple algebraic group of adjoint type over an algebraically closed field k bad characteristic. We show that its sheets conjugacy classes are parametrized by -conjugacy pairs $(M,{\mathcal O})$ where M is the identity component centralizer semisimple element in and ${\mathcal O}$ rigid unipotent class , analogy with good characteristic case.

Graded nilpotent Lie groups, or Carnot Groups are to subRiemannian geometry as Euclidean spaces are to Riemannian geometry. They are the metric tangent cones for this geometry. Hoping that the analogy between subRiemannian and Riemannian geometry is a strong one, one might conjecture that the subRiemannian geodesic flow on any Carnot group is completely integrable. We prove this conjecture is f...

The faithfulness of the orthogonal group case of Brauer’s representation of the Brauer centralizer algebras restricted to their Temperley-Lieb subalgebras, which was established by Vaughan Jones, is here proved in a new, elementary and self-contained, manner. Mathematics Subject Classification (2000): 57M99, 15A03, 16G99, 05C50

In this paper, we introduce the notation of soft bornological group to solve problem boundedness for group. We combine set theory with bornology space produce a new structure which is called So that both product and inverse maps are bounded. As well as, study actions on sets. The aim partition into orbital classes by acting set. addition, explain centralizer, normalizer, stabilizer in details. ...

In the representation theory, the classification and the construction of the irreducible representations are essential themes. In the first half of the twentieth century, I. Schur[11] introduced a prominent method to obtain the finite dimensional irreducible representations of the general linear group GL(n,C), or equivalently of its Lie algebra gl(n,C), which we call Schur-Weyl reciprocity at p...

Let G be a (not necessarily finite) group and p a finite dimensional faithful irreducible representation of G over an arbitrary field; write ~p for p viewed as a projective representation. Suppose that p is not induced (from any proper subgroup) and that ~p~ is not a tensor product (of projective representations of dimension greater than 1 ). Let AT be a noncentral subgroup which centralizes al...

A $p$-group $G$ is called a $mathcal{CAC}$-$p$-group if $C_G(H)/H$ is ‎cyclic for every non-cyclic abelian subgroup $H$ in $G$ with $Hnleq‎ ‎Z(G)$‎. ‎In this paper‎, ‎we give a complete classification of‎ ‎finite $mathcal{CAC}$-$p$-groups‎.

Alahmadi et al. (2017) [2] introduced the notion of twisted centralizer codes, C F q ( A , γ ) defined as = { X ∈ n × : } for and . Moreover, [3] also investigated dimension such codes obtained upper lower bounds dimension, exact value only cyclic or diagonalizable matrices Generalizing sharpening al.'s results, in this paper, we determine well provide an algorithm to construct explicit basis a...