CMA Research Report

MRR02-008

Some low degree generators of the integral cohomology ring of a non-abelian group of order p⁴ and exponent p

Abstract:  Let P denote the non-abelian group of order p³ and exponent p. It is known that H^*(P;Z) has two generators in degree 3 and no other odd degree generators. Let G denote the non-abelian group of order p⁴ and exponent p (p\geq 5) with two minimal generators. It is reasonable to ask whether the integral cohomology ring of G also has odd degree generators only in degree 3. In this paper we determine the additive structure of H^*(G;Z) up to degree 7 and show in particular that H^*(G;Z) not only has two generators in degree 3 but also two generators in degree 5 and one generator in degree 7 among its odd degree generators.

AMS Classification:  20J06
Date:  25 June 2002

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