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The linearity of wreath products

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  26 February 2010

B. A. F. Wehrfritz
B. A. F. Wehrfritz
Affiliation:
School of Mathematical Sciences, Queen Mary & Westfield College, Mile End Road, London El 4NS
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Extract

A long time ago Ju. E. Vapne ([2], [3]) and, independently, the author ([4], [5]) classified those standard and complete wreath products that have faithful representations of finite degree over (commutative) fields. See [6] pages 37 40 & 150–154 for an account of this. Recently, in connection with finitary linear groups, I needed a more general wreath product. Somewhat to my surprise neither the classification nor the proof for these generalized wreath products was a straightforward translation from the standard case. The situation is intrinsically more complex and it seems worthwhile recording it separately.

MSC classification

Secondary: 20E22: Extensions, wreath products, and other compositions
Type
Research Article
Information
Mathematika , Volume 44 , Issue 2 , December 1997 , pp. 357 - 367
Copyright
Copyright © University College London 1997

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References

1.Jacobson, N.. Structure of Rings (2nd ed.), Amer. Mart. Soc. Coloq. Pub. (Providence, R.I., 1964).Google Scholar
2.Vapne, Ju. E.. On the representability as matrices of the wreath product of groups (Russian). Mat. Zametki, 7 (1970), 181189.Google Scholar
3.Vapne, Ju. E.. The criterion for the representability of wreath products of groups by matrices (Russian). Dokl. Akad. Nauk SSSR, 195 (1970), 13–16. Soviet Math. Dokl. 11 (1970), 1396–1399.Google Scholar
4Wehrfritz, B. A. F.. Wreath products of linear groups—the characteristic-p case. Bull. London Math. Soc., 3 (1971). 331332.CrossRefGoogle Scholar
5.Wehrfritz, B. A. F.. Wreath products and chief factors in linear groups. J. London Math. Soc. (2), 4 (1972), 671681.CrossRefGoogle Scholar
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7.Wehrfritz, B. A. F.. Conjugacy separating representations of free groups. Proc. Amer. Math. Soc., 40 (1973), 5256.CrossRefGoogle Scholar