On exponents of homology and cohomology of finite groups

Carlson, Jon F.

doi:10.1090/S0002-9939-1988-0934848-6

On exponents of homology and cohomology of finite groups
HTML articles powered by AMS MathViewer

by Jon F. Carlson

Proc. Amer. Math. Soc. 102 (1988), 814-816

DOI: https://doi.org/10.1090/S0002-9939-1988-0934848-6

PDF | Request permission

Abstract:

Let $G$ be a finite group and let $r$ be the maximum of the $p$-ranks of $G$ for all primes $p$ dividing the order to $G$. There exist positive integers $m$ and $n$ such that the exponents of ${H^n}(G,{\mathbf {Z}})$ and ${H_m}(G,{\mathbf {Z}})$ are greater than $|G{|^{1/r}}$.

References

David J. Benson and Jon F. Carlson, Complexity and multiple complexes, Math. Z. 195 (1987), no. 2, 221–238. MR 892053, DOI 10.1007/BF01166459
William Browder, Cohomology and group actions, Invent. Math. 71 (1983), no. 3, 599–607. MR 695909, DOI 10.1007/BF02095996
Gene Lewis, The integral cohomology rings of groups of order $p^{3}$, Trans. Amer. Math. Soc. 132 (1968), 501–529. MR 223430, DOI 10.1090/S0002-9947-1968-0223430-6