The existence of Golod groups with infinite center
type: Item
instance of: scholarly article
title: The existence of Golod groups with infinite center
zbMATH Open document ID: 0603.20036
DOI: 10.1007/BF01156672
author: A. V. Timofeenko
published in: Mathematical Notes
publication date: 1986-01-01T00:00:00Z
review text: Let p be a prime number, and d be a natural number, \(d\geq 2\). Let F be the associative ring of polynomials without free members in non-commuting variables \(x_ 1,...,x_ d\) over the field GF(p). Let \(f_ 1\), \(f_ 2,..\). be homogeneous polynomials in F, I be the ideal generated by these elements, and \(r_ i\) be the number of polynomials of degree i in the sequence \(f_ 1\), \(f_ 2,..\). If \(r_ i\leq \epsilon^ 2(d- 2\epsilon)^{i-2}\), \(0<\epsilon <0,5\), and F/I is a nil-algebra, then the multiplicative group \(G_ I=gp(1+x_ 1+I,...,1+x_ d+I)\) is just the Golod group studied in this article where 1 is the unity of the field GF(p). It is proved that, for every prime number p and every natural number \(d\geq 2\), there exists a d-generated Golod p-group \(G_ I\) all of whose (d-1)-generated subgroups are finite such that its center \(Z(G_ I)\) is infinite.
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 3973160
zbMATH Keywords: infinite center
zbMATH Keywords: (d-1)-generated subgroups finite
zbMATH Keywords: d-generated Golod p- group
reviewed by: Ju. I. Merzljakov
MaRDI profile type: Publication
cites work: Q4745979
description: scientific article; zbMATH DE number 3973160