On Automorphisms and Wreath Products in Crossed Modules - Dehghani, M. A.; Davvaz, B. (Communications in Mathematics and Applications, 2017)
In this paper, we show that if \(W_1 = A_1W_rB_1\), \(W_2 = A_2W_rB_2\) are wreath products groups with \(A_i=B_i\), \(1\le i\le 2\) nontrivial, then \(Aut_C(W_1,W_2,\partial)=I_{nn}(W_1,W_2,\partial)\) if and only if \(A_i=B_i=C_2\), \(1\le i\le 2\). Moreover, we obtain some results for central automorphisms of crossed module \((W_1,W_2,\partial)\) when \(W_1\), \(W_2\) are wreath products groups.
Keywords: Crossed module; Central automorphism; Wreath product