We study reductive subgroups $H$ of a linear algebraic group $G$ -- possibly non-connected such that contains regular unipotent element $G$. show under suitable hypotheses, are $G$-irreducible in the sense Serre. This generalizes results Malle, Testerman and Zalesski. obtain analogous for Lie algebras finite groups type. Our proofs short, conceptual uniform.

‎in this paper some properties of weak regular injectivity for $s$-posets‎, ‎where $s$ is a pomonoid‎, ‎are studied‎. ‎the behaviour‎ ‎of different kinds of weak regular injectivity with products‎, ‎coproducts and direct sums is considered‎. ‎also‎, ‎some‎ ‎characterizations of pomonoids over which all $s$-posets are of‎ ‎some kind of weakly regular injective are obtained‎. ‎further‎, ‎we‎ ‎giv...

We give a necessary and sufficient condition for pair of parabolic subgroups $P$ $Q$ $G=GL_n(\mathbb{R})$ such that the tensor product any two unitarily induced representations from are tempered. also an $L^p$-estimate matrix coefficients regular on $L^2(G/L)$ when $L$ is Levi subgroup $G$.

In this paper, we introduce transposition regularity into AG-groupoids, and a variety of regular AG-groupoids (L1/R1/LR, L2/R2/L3/R3-groupoids) are obtained. Their properties structures discussed by their decomposition theorems: (1) L1/R1-transposition equivalent to each other, they can be decomposed the union disjoint Abelian subgroups; (2) LR-transposition an example is given illustrate that ...

We parametrize the space of double cosets group GL(n,k) with respect to two subgroups T−, T+ block strictly triangular matrices. In appendix, we consider quasi-regular representation GL(n,C) in L2 on T−∖GL(n,C), observe that it admits an additional symmetries, find joint spectrum, and is multiplicity free.

We study the subgroup structure of discrete groups that share cohomological properties which resemble non-negative curvature. Examples include all Gromov hyperbolic groups. We provide strong restrictions on the possible s-normal subgroups of a ’negatively curved’ group. Another result says that the image of a group, which is boundedly generated by a finite set of amenable subgroups, in a group,...

Let G be a finite almost simple group with socle G0. A (nontrivial) factorization of is an expression the form G=HK, where factors H and K are core-free subgroups. There extensive literature on factorizations groups, important applications in permutation theory algebraic graph theory. In recent paper, Xia second-named author describe groups solvable factor H. Several infinite families arise con...

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We describe all left braces of size 8p for an odd prime p?3,7 and validate the number given by Bardakov, Neschadim Yadav in [2]. give a characterization isomorphism classes semidirect product then description is done first describing 8, as conjugacy regular subgroups corresponding holomorph, checking how many non isomorphic are obtained from each one them.