On Automorphisms and Wreath Products in Crossed Modules

Authors

  • M. A. Dehghani Department of Mathematics, Yazd University, Yazd
  • B. Davvaz Department of Mathematics, Yazd University, Yazd

DOI:

https://doi.org/10.26713/cma.v8i3.394

Keywords:

Crossed module, Central automorphism, Wreath product

Abstract

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.

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References

M. Alp, Christopher D. Wenseley, Automorphisms and homotopies of groupoids and crossed modules, Appl. Categor Struct., 18 (2010), 473-504.

M. Alp, Actor of crossed modules of algebroids, Proc. 16th Int. Conf. Jangjeon Math. Soc., 16 (2005), 6-15.

G. Baumslag, Wreath products and p-groups. Proc. Cambridge phill. Soc., 55 (1959), 224-231.

C. H. Houghton, On the automorphism groups of certain wreath products, Publ. Math. Debrecen, 9 (1963) 307-313.

P. M. Neumann, On the structure of standard wreath products of groups, Math. Z., 84 (1964), 343-373.

K. Norrie, Actions and automorphisms of crossed modules, Bull. Soc. Math. France, 118 (1990) 129-146.

J. Panagopoulos, The groups of central automorphisms of the standard wreath products, Arch. Math., 45 (1985) 411-417.

J. H. C. Whitehead, Combinatorial homotopy II, Bull. Amer. Math. Soc. 55 (1949) 453-496.

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Published

30-12-2017
CITATION

How to Cite

Dehghani, M. A., & Davvaz, B. (2017). On Automorphisms and Wreath Products in Crossed Modules. Communications in Mathematics and Applications, 8(3), 315–322. https://doi.org/10.26713/cma.v8i3.394

Issue

Section

Research Article