Geodesic
Direct Product Decompositions of Twisted Wreath Products
Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 163-172

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DOI

The twisted wreath product of two groups was first defined by B. H. Neumann ([1]) who used this construction to present a group-theoretic proof of a theorem due to Auslander and Lyndon. In this paper we present a complete characterization of the direct product decompositions of a restricted twisted wreath product of two groups A and B provided this product is not simply a semi-direct product of A by B. 
Brown, Jeffrey M. Direct Product Decompositions of Twisted Wreath Products. Canadian mathematical bulletin, Tome 18 (1975) no. 2, pp. 163-172. doi: 10.4153/CMB-1975-033-x
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     title = {Direct {Product} {Decompositions} of {Twisted} {Wreath} {Products}},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-033-x/}
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