- Journal of New Results in Science
- Vol: 10 Issue: 1
- n-complete crossed modules and wreath products of groups
n-complete crossed modules and wreath products of groups
Authors : M. A. Dehghani, B. Davvaz
Pages : 38-45
View : 15 | Download : 8
Publication Date : 2021-04-30
Article Type : Research
Abstract :In this paper we examine the $n$-completeness of a crossed module and we show that if $X=(W_1,W_2,\partial)$ is an $n$-complete crossed module, where $W_i=A_i wr B_i$ is the wreath product of groups $A_i$ and $B_i$, then $A_i$ is at most $n$-complete, for $i=1,2.$ Moreover, we show that when $X=(W_1,W_2,\partial)$ is an $n$-complete crossed module, where $A_i$ is nilpotent and $B_i$ is nilpotent of class $n$, for $i=1,2$, then if $A_i$ is an abelian group, then it is cyclic of order $p_i.$ Also, if $W_i=C_ pwr C_2$, where $p$ is prime with $p>3$, $i=1,2$, then $X=(W_1,W_2,\partial)$ is not an $n$-complete crossed module.Keywords : crossed module, wreath products, commutator