Open AccessArcs in Locally Compact Groups
Author(s) -
Andrew M. Gleason
Publication year - 1950
Publication title -
proceedings of the national academy of sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 5.011
H-Index - 771
eISSN - 1091-6490
pISSN - 0027-8424
DOI - 10.1073/pnas.36.11.663
Subject(s) - nucleic acid , small molecule , nucleic acid structure , molecule , chemistry , biophysics , conformational change , biochemistry , computational biology , biology , rna , gene , organic chemistry
THEOREM 7. IfK is reducible to L and K' to L', then K 0 L is reducible to K' 0 L'. THEOREM 8. For a direct sum I1 + 112 of abelian groups H1 and II2, A0(H11 + II2) is reducible to A0(1) 0 A0(II2). Together with Theorem 2 and the results for cyclic groups, these Theorems prove THEOREM 9. If 11 is a finitely generated abelian group, then any abelian homology or cohomology group A,(II) or Af(II, J) may be computed in a finite number of steps. In certain cases, the results can be put into invariant form. Thus for any abelian group II (not necessarily finitely generated) we have
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