Bounds On the order of the Schur multiplier of p-groups
نویسندگان
چکیده
In 1956, Green provided a bound on the order of Schur multiplier p-groups. This bound, given as function group, is best possible. Since then, has been refined numerous times by adding other inputs to function, such as, minimal number generators group and derived subgroup. We strengthen these bounds another input, group's nilpotency class. The specific cases class 2 maximal are discussed in greater detail.
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...
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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...
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A 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...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2024
ISSN: ['1873-1376', '0022-4049']
DOI: https://doi.org/10.1016/j.jpaa.2023.107463