Following Malcev [5], we will call a subgroup M of a group G finitely separable if for any element g ∈ G, not belonging to M, there exists a homomorphism φ of group G onto some finite group X such that gφ / ∈Mφ. This is equivalent to the statement that for any element g ∈ G \M, there exists a normal subgroup N of finite index in G such that g / ∈MN . A group G is subgroup separable if each of i...

let $g$ be a finite $p$-soluble group‎, ‎and $p$ a sylow $p$-subgroup of $g$‎. ‎it is proved‎ ‎that if all elements of $p$ of order $p$ (or of order ${}leq 4$ for $p=2$) are‎ ‎contained in the $k$-th term of the upper central series of $p$‎, ‎then the $p$-length of‎ ‎$g$ is at most $2m+1$‎, ‎where $m$ is the greatest integer such that‎ ‎$p^m-p^{m-1}leq k$‎, ‎and the exponent of the image of $p$...

a subgroup $h$ is said to be $nc$-supplemented in a group $g$ if there exists a subgroup $kleq g$ such that $hklhd g$ and $hcap k$ is contained in $h_{g}$, the core of $h$ in $g$. we characterize the supersolubility of finite groups $g$ with that every maximal subgroup of the sylow subgroups is $nc$-supplemented in $g$.

Abstract. The multiplier representation of the generalized symmetry group of a quasiperiodic flow on the n-torus defines, for each subgroup of the multiplier group of the flow, a group invariant of the smooth conjugacy class of that flow. This group invariant is the internal semidirect product of a subgroup isomorphic to the n-torus by a subgroup isomorphic to that subgroup of the multiplier gr...

We study the generalized Whittaker models for G = GSp(2,R) associated with indefinite binary quadratic forms when they arise from two standard representations of G: (i) a generalized principal series representation induced from the non-Siegel maximal parabolic subgroup and (ii) a (limit of) large discrete series representation. We prove the uniqueness of such models with moderate growth propert...

For a finite group G and an arbitrary prime p, let S (G) denote the P intersection of all maximal subgroups M of G such that [G:M] is both composite and not divisible by p; if no such M exists we set S (G) G. Some properties of P G are considered involving S (G). In particular, we obtain a characterization of P G when each M in the definition of S (G) is nilpotent. P