maximal subsets of pairwise non-commuting elements of p-groups of order less than p^6
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abstract
let $g$ be a non-abelian group of order $p^n$, where $nleq 5$ in which $g$ is not extra special of order $p^5$. in this paper we determine the maximal size of subsets $x$ of $g$ with the property that $xyneq yx$ for any $x,y$ in $x$ with $xneq y$.
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maximal subsets of pairwise non-commuting elements of $p$-groups of order less than $p^6$
let $g$ be a non-abelian group of order $p^n$, where $nleq 5$ in which $g$ is not extra special of order $p^5$. in this paper we determine the maximal size of subsets $x$ of $g$ with the property that $xyneq yx$ for any $x,y$ in $x$ with $xneq y$.
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full textmaximal subsets of pairwise non-commuting elements of some finite p-groups
let g be a group. a subset x of g is a set of pairwise noncommuting elements if xy ̸= yx for any two distinct elements x and y in x. if |x| ≥ |y | for any other set of pairwise non-commuting elements y in g, then x is said to be a maximal subset of pairwise non-commuting elements. in this paper we determine the cardinality of a maximal subset of pairwise non-commuting elements in any non-abelian...
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15 صفحه اولMaximal non-commuting subsets of groups
Given a finite group G, we consider the problem of finding the maximal size nc(G) of subsets of G that have the property that no two of their elements of commute. After constructing a large noncommuting subset of Sn, we consider the definition and classification of extraspecial p-groups and focus on such a group: S(p.n). We show that nc(S(2, n)) = 2n+ 1 and that S(p, n) ≥ pn+ 1.
full textPairwise non-commuting elements in finite metacyclic $2$-groups and some finite $p$-groups
Let $G$ be a finite group. A subset $X$ of $G$ is a set of pairwise non-commuting elements if any two distinct elements of $X$ do not commute. In this paper we determine the maximum size of these subsets in any finite non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup.
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Journal title:
international journal of group theoryPublisher: university of isfahan
ISSN 2251-7650
volume 3
issue 1 2014
Keywords
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