An application of Burnside rings in elementary finite group theory
نویسندگان
چکیده
منابع مشابه
The Brauer group of Burnside rings
The Brauer group of a commutative ring is an important invariant of a commutative ring, a common journeyman to the group of units and the Picard group. Burnside rings of finite groups play an important rôle in representation theory, and their groups of units and Picard groups have been studied extensively. In this short note, we completely determine the Brauer groups of Burnside rings: they van...
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We define the cohomological Burnside ring B(G,M) of a finite group G with coefficients in a ZG-module M as the Grothendieck ring of the isomorphism classes of pairs [X, u] where X is a G-set and u is a cohomology class in a cohomology group H X(G,M). The cohomology groups H ∗ X(G,M) are defined in such a way that H∗ X(G, M) ∼= ⊕iH∗(Hi,M) when X is the disjoint union of transitive G-sets G/Hi. I...
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1 Let G be a finite group. The Burnside ring B(G) of the group G is one of the fundamental representation rings of G, namely the ring of permutation representations. It is in many ways the universal object to consider when looking at the category of G-sets. It can be viewed as an analogue of the ring Z of integers for this category. It can be studied from different points of view. First B(G) is...
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Using the Burnside ring theoretic methods a new setting and a complete description of the Artin exponent A(G) of finite p-groups was obtained in [4]. In this paper, we compute A(G) for any finite group G – hence providing the global version of [4].
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 1992
ISSN: 0001-8708
DOI: 10.1016/0001-8708(92)90008-9