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

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

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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

Vol. 8 No. 3 (2017)

Section

Research Article

License

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