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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Homology in varieties of groups. I


Author: C. R. Leedham-Green
Journal: Trans. Amer. Math. Soc. 162 (1971), 1-14
MSC: Primary 20.50; Secondary 18.00
DOI: https://doi.org/10.1090/S0002-9947-1971-99930-9
Part II: Trans. Amer. Math. Soc. (1971), 15-25
Part III: Trans. Amer. Math. Soc. (1971), 27-33
MathSciNet review: 0284510
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Abstract: Well-known techniques allow one to construct a (co-) homology theory relative to a variety. After two paragraphs which discuss the modules to be considered and the construction of the (co-) homology groups, we come to our main homological result, namely that the theory is not always equivalent to a Tor or Ext. In the fourth paragraph we prove our main group-theoretic result; two covering groups of a finite group generate the same variety ``up to exponent". Finally we produce a restricted version of the Künneth formula.


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DOI: https://doi.org/10.1090/S0002-9947-1971-99930-9
Keywords: Variety of groups, (co-) homology of groups, triple homology, Kan extension, Rinehart's exact sequence, Fox derivative, group extension, Schur multiplier, covering group, Künneth formula
Article copyright: © Copyright 1971 American Mathematical Society

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