Groups with many rewritable products

Authors:
Mario Curzio, Patrizia Longobardi, Mercede Maj and Akbar Rhemtulla

Journal:
Proc. Amer. Math. Soc. **115** (1992), 931-934

MSC:
Primary 20F24

MathSciNet review:
1086580

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Abstract: For any integer , denote by the class of groups in which every infinite subset contains elements such that the product for some permutation . The case was studied by B. H. Neumann who proved that is precisely the class of centre-by-finite groups. Here we show that for some if and only if contains an *FC*-subgroup of finite index such that the exponent of is finite, where denotes the centre of .

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1992-1086580-X

Article copyright:
© Copyright 1992
American Mathematical Society