2-nilpotent multiplier of 2-groups of maximal class
Subject Areas : AlgebraSaeed Alakbi 1 , S. Hadi Jafari 2
1 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
Keywords: گروه پوچتوان, ضربگر 2- پوچتوان, گروه چهارگان تعمیم یافته, گروه دووجهی و و گروه نیمه دووجهی,
Abstract :
There has been a great importance in understanding the nilpotent multipliers of finite groups in recent past. Let a group G be presented as the quotient of a free group F by a normal subgroup R. Given a positive integer c, the c-nilpotent multiplier of the group G is the abelian group M^{(c)}(G)=(R\cap \gamma_{c+1}(F))/\gamma_{c+1}(R,F). In particular, M^(1)(G) is the Schur multiplier of G. One motivation to study the c-nilpotent multipliers is its relevance to the isologism theory of P. Hall, in which groups can be classified into isologism classes. Another important reason is that, determining the structures of c-nilpotent multipliers is essential in studying generalized capability and covering groups, and would be generally useful in developing such a framework. In this paper we describe the structure of 2-nilpotent multiplier of finite 2-groups of maximal class. In particular, we give some relations about the generators of their triple tensor product and triple exterior product.
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