Exterior and symmetric (co)homology of groups

TL;DR

This paper explores exterior and symmetric (co)homologies of groups, introducing symmetric homology, computing these for finite groups, comparing them with classical cohomology, and establishing related homomorphisms.

Contribution

It introduces symmetric homology of groups and provides computations and comparisons with classical (co)homologies, along with homomorphism constructions.

Findings

Computed exterior and symmetric (co)homologies for some finite groups

Compared classical, exterior, and symmetric (co)homologies

Derived restriction and corestriction homomorphisms for exterior cohomology

Abstract

The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite groups. We also compare the classical, exterior and symmetric (co)homologies. Finally, we derive restriction and corestriction homomorphisms for exterior cohomology