Groups with infinite mod-p Schur multiplier
نویسندگان
چکیده
منابع مشابه
on the order of the schur multiplier of a pair of finite $p$-groups ii
let $g$ be a finite $p$-group and $n$ be a normal subgroup of $g$ with $|n|=p^n$ and $|g/n|=p^m$. a result of ellis (1998) shows that the order of the schur multiplier of such a pair $(g,n)$ of finite $p$-groups is bounded by $ p^{frac{1}{2}n(2m+n-1)}$ and hence it is equal to $ p^{frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$. recently, the authors have characterized...
متن کاملon the order of the schur multiplier of a pair of finite p-groups ii
let $g$ be a finite $p$-group and $n$ be a normal subgroup of $g$ with $|n|=p^n$ and $|g/n|=p^m$. a result of ellis (1998) shows that the order of the schur multiplier of such a pair $(g,n)$ of finite $p$-groups is bounded by $ p^{frac{1}{2}n(2m+n-1)}$ and hence it is equal to $ p^{frac{1}{2}n(2m+n-1)-t}$ for some non-negative integer $t$. recently, the authors have characterized...
متن کاملA note on the order of the Schur multiplier of p-groups
Let G be a finite p-group of order pn with |G′| = pk, and let M(G) denote its Schur multiplier. A classical result of Green states that |M(G)| ≤ p 1 2 n(n−1) . In 2009, Niroomand, improving Green’s and other bounds on |M(G)| for a non-abelian p-group G, proved that |M(G)| ≤ p 2 (n−k−1)(n+k−2)+1. In this paper, we prove that a bound, obtained earlier by Ellis and Wiegold, is stronger than that o...
متن کاملTHE MOD p REPRESENTATION THEORY OF p - ADIC GROUPS
Exercise 1 (Maximal compact subgroups of G). A lattice in Qp is a finitelygenerated Zp-submodule of Qp that generates Qp as vector space. In particular, it’s free of rank n. Note that G acts transitively on the set of lattices in Qp . (i) Show that K = StabG(Zp ). (ii) Suppose that K ′ is a compact subgroup of G. Show that K ′ stabilises a lattice. (Hint: show that the K ′-orbit of Zp is finite...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2011
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2011.06.033