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On groups which are residually 
-commutative
Published online by Cambridge University Press: 20 January 2009
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In this paper we study a property which we call residual -commutativity. This idea was kindled by a paper of Ayoub (1) and one of Stanley (6). Durbin has defined a similar property in (2) which has also been studied by Slotterbeck in (4). Durbin's property implies residual -commutativity but we have not been able to decide if they are equivalent. However, we have shown that they coincide in certain circumstances. The notation, unless otherwise stated, is that of Robinson (3).
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- Research Article
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- Copyright © Edinburgh Mathematical Society 1976
References
REFERENCES
(1) Ayoub, C., On properties possessed by solvable and nilpotent groups, J. Australian Math. Soc. 9 (1969), 218–227.CrossRefGoogle Scholar
(2) Durbin, J. R., On normal factor coverings of groups, J. Algebra 12 (1969), 191–194.CrossRefGoogle Scholar
(3) Robinson, D. J. S., Finiteness conditions for generalized soluble groups, parts 1 and 2 (Springer-Verlag, Berlin-Heidelberg-New York, 1972).CrossRefGoogle Scholar
(4) Slotterbeck, O. A., Finite factor coverings of groups, J. Algebra 17 (1971), 67–73.CrossRefGoogle Scholar
(5) Stanley, T. E., Generalizations of the classes of nilpotent and hypercentral groups, Math. Z. 118 (1970), 180–190.CrossRefGoogle Scholar
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