Splitting theorem for homology of
Author:
Stanisław Betley
Journal:
Proc. Amer. Math. Soc. 108 (1990), 297-302
MSC:
Primary 20J05
DOI:
https://doi.org/10.1090/S0002-9939-1990-0984782-X
MathSciNet review:
984782
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: It is proved that if is a stable system of coefficients for
and
contains
, then for any
, the group
contains
as a direct summand. Now let
act on
(matrices over
) by conjugation. Then our theorem implies that the trace map
is a split epimorphism on homology.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1990-0984782-X
Keywords:
Homology of a group,
stable system of coefficients
Article copyright:
© Copyright 1990
American Mathematical Society