we call $h$ an $ss$-embedded subgroup of $g$ if there exists a‎ ‎normal subgroup $t$ of $g$ such that $ht$ is subnormal in $g$ and‎ ‎$hcap tleq h_{sg}$‎, ‎where $h_{sg}$ is the maximal $s$-permutable‎ ‎subgroup of $g$ contained in $h$‎. ‎in this paper‎, ‎we investigate the‎ ‎influence of some $ss$-embedded subgroups on the structure of a‎ ‎finite group $g$‎. ‎some new results were obtained.

We apply Voronoi’s algorithm to compute representatives of the conjugacy classes of maximal finite subgroups of the unit group of a maximal order in some simple Q-algebra. This may be used to show in small cases that non-conjugate orders have non-isomorphic unit groups.

This note is intended as a supplement and clarification to the proof of Theorem 3.3 of [1]; namely, it is consistent that b = ℵ 1 yet for every ultrafilter U on ω there is a ≤ * chain {f ξ : ξ ∈ ω 2 } such that {f ξ /U : ξ ∈ ω 2 } is cofinal in ω/U. The general outline of the the proof remains the same. In other words, a ground model is taken which satisfies 2 ℵ0 = ℵ 1 and in which there is a ♦...

Introduction. Dedekind has determined all groups whose subgroups are all normal (see, e.g., [5, Theorem 12.5.4]). Partially generalizing this, Wielandt showed that a finite group is nilpotent, if and only if all its subgroups are subnormal, and also if and only if all maximal subgroups are normal [5, Corollary 10.3.1, 10.3.4]. Huppert [7, Sätze 23, 24] has shown that if all 2nd-maximal subgroup...

‎‎in cite{fr 1‎, ‎fr 2} using faithful complex representations of cyclically pinched and conjugacy pinched one-relator groups we proved that any limit group has a faithful representation in $psl(2,c)$‎. ‎further this representation can be effectively constructed using the jsj decomposition‎. ‎in this note we show that any hyperbolic cyclically pinched one-relator group with maximal amalgamated ...

Let $G$ be an infinite-dimensional representation-theoretic Kac--Moody group associated to a nonsingular symmetrizable generalized Cartan matrix. We consider Eisenstein series on induced from unramified cusp forms finite-dimensional Levi subgroups of maximal parabolic subgroups. Under natural condition subgroups, we prove that the cuspidal are entire full complex plane.