On Automorphisms and Wreath Products in Crossed Modules

M. A. Dehghani, B. Davvaz


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.


Crossed module; Central automorphism; Wreath product

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