On the integral cohomology of a sylow subgroup of the symmetric group

Cárdenas, Humberto; Lluis, Emilio

doi:10.1080/00927879008823904

Cited by 6 publications

(4 citation statements)

References 2 publications

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“…On the other hand, t is bounded above by the minimal degree of a cohomology element of H * (G, k) whose restriction to the center Z of P is not nilpotent (see the proof of Theorem 3.1 of [5]). Now by the analysis of [4] (see Proposition 5.1) there is an element γ in degree 2p(p − 1) in integral cohomology whose restriction to Z is not zero. Because Z is cyclic and γ has even degree this element is not nilpotent and thus γ restricts to a nonzero element in the mod-p cohomology.…”

Section: Torsion Free Complementsmentioning

confidence: 99%

Endotrivial modules for the symmetric and alternating groups

Carlson¹,

Mazza

Nakano³

2009

Proceedings of the Edinburgh Mathematical Society

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Section: Torsion Free Complementsmentioning

confidence: 99%

Endotrivial modules for the symmetric and alternating groups

Carlson¹,

Mazza

Nakano³

2009

Proceedings of the Edinburgh Mathematical Society

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“…That is, P(0 is the Poincare series ofH*(G, F^). The following relation between P(£) and 0(0 has been proven in [1]. We give a proof here for the sake of completeness.…”

Section: We Havementioning

confidence: 79%

The Cohomology Rings of Some $p$-Groups

Chin

1995

Publ. Res. Inst. Math. Sci.

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We determine the mod-p cohomology ring and some of the integral cohomology ring structure of a p-group expressible as an extension with kernel cyclic of order p and quotient C p m 0 C p n, where m, n > 1. § 1. IntroductionLet p denote an odd prime and let P m n be the group with presentation of the formwhere m, n > 1. We may express P m n as a central extension of the formwhere C = = C p and L = (A, B} = C p m X C p n. In this paper we shall determine the mod-p cohomology ring and some of the integral cohomology ring structure of P m n when m,n>l. For the case when m = n = 1, P ltl is the non-abelian group of order p 3 and exponentp, and the integral and mod-p cohomology rings of P l { are known (see [4], [5], [7]). We note that for £ = 3 and m, n > 1, Leary in [6] has obtained the Poincare series of H*(P m n , F 3 ). Let G = P m> " where m, n > 1. It is clear that we may assume, without loss of generality, that m > n > 2. In section 2 of this paper we shall review some facts on Massey products. Then in section 3, we shall use Massey products to define some generators of degree two in the mod-p cohomology ring of G and to determine some of the relations involving these generators. This explicit use of Massey products to obtain the cohomology ring structure has been demonstrated by Leary in [3] and [5]. We remark here that the mod-p cohomology ring structure of G

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“…• Remarks. Lluis and Cárdenas have found the additive structure of the cohomology of C 3 wreath C 3 [4], and many authors have studied the cohomology of the metacyclic groups. A similar result to Corollary 11 holds for the groups of order 16, but N. Yagita has exhibited a pair of groups of order p 4 for all p ≥ 5 having isomorphic integral cohomology groups [19].…”

Section: Cohomologymentioning

confidence: 99%