THE UPPER CENTRAL SERIES OF A p–GROUP ACTING ON A BOUNDED ABELIAN p-GROUP
نویسندگان
چکیده
We determine the upper central series of the maximal normal p–subgroup of the automorphism group of a bounded abelian p–group.
منابع مشابه
A NEW ALGORITHM FOR FINDING THE NILPOTENCY CLASS OF A FINITE p-GROUP DESCRIBING THE UPPER CENTRAL SERIES
In this paper we describe an algorithm for finding the nilpotency class, and the upper central series of the maximal normal p-subgroup ∆(G) of the automorphism group, Aut(G) of a bounded (or finite) abelian p-group G. This is the first part of two papers devoted to compute the nilpotency class of ∆(G) using formulas, and algorithms that work in almost all groups. Here, we prove that for p ≥ 3 t...
متن کاملOn equality of absolute central and class preserving automorphisms of finite $p$-groups
Let $G$ be a finite non-abelian $p$-group and $L(G)$ denotes the absolute center of $G$. Also, let $Aut^{L}(G)$ and $Aut_c(G)$ denote the group of all absolute central and the class preserving automorphisms of $G$, respectively. In this paper, we give a necessary and sufficient condition for $G$ such that $Aut_c(G)=Aut^{L}(G)$. We also characterize all finite non-abelian $p$-groups of order $p^...
متن کاملOn the Exponent of Triple Tensor Product of p-Groups
The non-abelian tensor product of groups which has its origins in algebraic K-theory as well as inhomotopy theory, was introduced by Brown and Loday in 1987. Group theoretical aspects of non-abelian tensor products have been studied extensively. In particular, some studies focused on the relationship between the exponent of a group and exponent of its tensor square. On the other hand, com...
متن کاملOn continuous cohomology of locally compact Abelian groups and bilinear maps
Let $A$ be an abelian topological group and $B$ a trivial topological $A$-module. In this paper we define the second bilinear cohomology with a trivial coefficient. We show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. Also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...
متن کاملAn explicit formula for the number of fuzzy subgroups of a finite abelian $p$-group\ of rank two
Ngcibi, Murali and Makamba [Fuzzy subgroups of rank two abelian$p$-group, Iranian J. of Fuzzy Systems {bf 7} (2010), 149-153]considered the number of fuzzy subgroups of a finite abelian$p$-group $mathbb{Z}_{p^m}times mathbb{Z}_{p^n}$ of rank two, andgave explicit formulas for the cases when $m$ is any positiveinteger and $n=1,2,3$. Even though their method can be used for thecases when $n=4,5,l...
متن کامل