Some properties of E(G, W, F(T)G) and an application in the theory of splittings of groups

Author(s)

Fanti, E. L. C. ^[1] ; Silva, L. S. ^[2]

Affiliation

^[1] Sao Paulo State Univ, UNESP, Dept Math, IBILCE, R Cristovao Colombo 2265, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

^[2] IFSP Fed Inst Technol Sao Paulo, Av Univ 145, BR-17607220 Tupa, SP - Brazil

• Document type: Journal article
• Source: ALGEBRA & DISCRETE MATHEMATICS; v. 30, n. 2, p. 179-193, 2020.
• Web of Science Citations: 0

Abstract

Let us consider W a G-set and M a Z(2)G-module, where G is a group. In this paper we investigate some properties of the cohomological the theory of splittings of groups. Namely, we give a proof of the invariant E(G, W, M), defined in {[}5] and present related results with independence of E(G, W, M) with respect to the set of G-orbit representatives in W and properties of the invariant E(G, W, F(T)G) establishing a relation with the end of pairs of groups e e(G, T), defined by Kropphller and Holler in {[}15]. The main results give necessary conditions for G to split over a subgroup T, in the cases where M = Z(2)(G/T) or M = F(T)G (AU)

• FAPESP's process: 12/24454-8 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 16/24707-4 - Algebraic, geometric and differential topology
• Grantee: Daciberg Lima Gonçalves
• Support Opportunities: Research Projects - Thematic Grants