maximal subsets of pairwise non-commuting elements of some finite p-groups
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abstract
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 p-groups with central quotient of order less than or equal to p3 for any prime number p. as an immediate consequence we give this cardinality for any non-abelian group of order p4.
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فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...
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.
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Journal title:
bulletin of the iranian mathematical societyPublisher: iranian mathematical society (ims)
ISSN 1017-060X
volume 39
issue 1 2013
Keywords
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