MAXIMAL SUBSETS OF PAIRWISE NONCOMMUTING ELEMENTS OF SOME p-GROUPS OF MAXIMAL CLASS
نویسندگان
چکیده
منابع مشابه
Maximal 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...
متن کاملmaximal 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...
متن کاملmaximal 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 $xneq y$.
متن کاملmaximal 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 $xneq y$.
متن کاملAutomorphisms of P-groups of Maximal Class
Juhász has proved that the automorphism group of a group G of maximal class of order p, with p ≥ 5 and n > p + 1, has order divisible by p. We show that by translating the problem in terms of derivations, the result can be deduced from the case where G is metabelian. Here one can use a general result of Caranti and Scoppola concerning automorphisms of two-generator, nilpotent metabelian groups.
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2011
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972711002401