On cohomologically Trivially modules over finite p-groups

2025/10/23 by Guerboussa, Yassine, Guedri, Maria
#20D15 #20J06 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2510.20418

Abstract

We show that every finitely generated cohomologically trivial module over RG, where G is a finite p-group and R is a p-adic ring, splits as the direct sum of a finite cohomologically trivial RG-module and a free RG-module. Along the way, we also establish other results concerning generators and relators of such modules.

Citations

• Non-inner automorphisms of order p in finite p-groups admitting cyclic center
• The quotients of the p-adic group ring of a cyclic group of order p
• On the cohomological triviality of the center of the Frattini subgroup
• Powerful p-groups have noninner automorphisms of order p and some cohomology
• Functional equations for zeta functions of groups and rings

Related

• A Splitting Theorem for Local Cohomology and its Applications
• Constructing modules with prescribed cohomological support
• On Modules over a G-set
• Finite generation of cohomology of finite groups
• On the BP<n>-cohomology of elementary abelian p-groups