On the Brauer monoid of \(S_3\). (English) Zbl 1107.12004

In the paper [D. Haile, R. Larson, M. Sweedler, Am. J. Math. 105, 689–814 (1983; Zbl 0523.13005)], it was shown that the Brauer monoid of a finite Galois group can be decomposed into a disjoint union of smaller groups. Each of these groups can be computed using Stimets’ methods (see [R. Stimets, Commun. Algebra 28, 1285–1308 (2000; Zbl 0969.12002) and “Relative weak cohomology extensions”, J. Algebra (to appear)] for details). However, this method involves difficult computations even for small order Galois groups. In the paper under review, the author applies Stimets’ method to certain idempotent weak 2-cocycles on \(S_3\).


12G05 Galois cohomology
16K50 Brauer groups (algebraic aspects)
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