The central series for Peiffer commutators in groups with operators
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چکیده
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The Homology of Peiffer Products of Groups
The Peiffer product of groups first arose in work of J.H.C. Whitehead on the structure of relative homotopy groups, and is closely related to problems of asphericity for two-complexes. We develop algebraic methods for computing the second integral homology of a Peiffer product. We show that a Peiffer product of superperfect groups is superperfect, and determine when a Peiffer product of cyclic ...
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The main objectives of this paper are to give general proofs of the following two facts: A. For an operad O in Ab, let A be a simplicial O-algebra such that Am is the O-subalgebra generated by ( ∑m i=0 si(Am−1)), for every n, and let NA be the Moore complex of A. Then d(NmA) = ∑
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Commutators originated over 100 years ago as a by-product of computing group characters of nonabelian groups. They are now an established and immensely useful tool in all of group theory. Commutators became objects of interest in their own right soon after their introduction. In particular, the phenomenon that the set of commutators does not necessarily form a subgroup has been well documented ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1990
ISSN: 0021-8693
DOI: 10.1016/0021-8693(90)90066-w