No CrossRef data available.
Article contents
A direct proof of Leutbecher's Lemma
Published online by Cambridge University Press: 18 May 2009
Extract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Using the theory of group extensions, A. Leutbecher [1] proved this
Lemma. Let G bea group, and w some 2-cocycle of a trivial G-module M. The cohomology class ofw will contain symmetric cocycles if and only if w is semisymmetric.
Here we have called w symmetric or semisymmetric according as w(h, g) = w(g, h) for all g, h ∈G or only for those with hg = gh. In one direction, the proof reduces to observing that 2-coboundaries of trivial G-modules are semisymmetric. The nontrivial part of the lemma also admits of a straightforward proof, as follows.
- Type
- Research Article
- Information
- Copyright
- Copyright © Glasgow Mathematical Journal Trust 1972
References
REFERENCES
1.Leutbecher, A., Über Automorphiefaktoren und die Dedekindschen Summen, Glasgow Math. J. 11 (1970), 41–57.CrossRefGoogle Scholar
2.Petersson, H., Zur analytischen Theorie der Grenzkreisgruppen, Teil I, Math. Ann. 115 (1937), 23–67.CrossRefGoogle Scholar
You have
Access