The cohomology ring of certain families of periodic virtually cyclic groups
S\'ergio Tadao Martins, Daciberg Lima Gon\c{c}alves, M\'arcio de, Jesus Soares

TL;DR
This paper computes the integral cohomology rings of specific virtually cyclic groups, revealing their periodic Farrell cohomology, which advances understanding of their algebraic topology.
Contribution
It provides explicit calculations of the cohomology rings for certain families of virtually cyclic groups, a novel contribution to algebraic topology.
Findings
Computed integral cohomology rings for the groups
Established periodicity in Farrell cohomology for these groups
Enhanced understanding of the algebraic structure of these groups
Abstract
Let G be a virtually cyclic of the form (Z_a x Z_b) x Z or [Z_a x (Z b x Q_{2^i})] x Z. We compute the integral cohomology ring of G, and then obtain the periodicity of the Farell cohomology of these groups.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Geometric and Algebraic Topology · Algebraic structures and combinatorial models
