Back to Search
Start Over
Homotopy theory and generalized dimension subgroups
- Publication Year :
- 2015
-
Abstract
- Let $G$ be a group and $R,S,T$ its normal subgroups. There is a natural extension of the concept of commutator subgroup for the case of three subgroups $\|R,S,T\|$ as well as the natural extension of the symmetric product $\|\bf r,\bf s,\bf t\|$ for corresponding ideals $\bf r,\bf s, \bf t$ in the integral group ring $\mathbb Z[G]$. In this paper, it is shown that the generalized dimension subgroup $G\cap (1+\|\bf r,\bf s,\bf t\|)$ has exponent 2 modulo $\|R,S,T\|.$ The proof essentially uses homotopy theory. The considered generalized dimension quotient of exponent 2 is identified with a subgroup of the kernel of the Hurewicz homomorphism for the loop space over a homotopy colimit of classifying spaces.<br />Comment: 18 pages
- Subjects :
- Mathematics - Group Theory
Mathematics - Algebraic Topology
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1506.08324
- Document Type :
- Working Paper