n-complete crossed modules and wreath products of groups

Authors : Ma DEHGHANİ, B DAVVAZ

Pages : 38-45

View : 18 | Download : 15

Publication Date : 2021-04-30

Article Type : Research Paper

Abstract :In this paper we examine the $n$-completeness of a crossed module and we show that if $X=insert ignore into journalissuearticles values(W_1,W_2,\partial);$ 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 $X=insert ignore into journalissuearticles values(W_1,W_2,\partial);$ 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 $X=insert ignore into journalissuearticles values(W_1,W_2,\partial);$ is not an $n$-complete crossed module.
Keywords : crossed module, wreath products, commutator