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Title: Systems of elements preserving measure on varieties of groups

It is proved that for any l, 1≤l≤r, a system of elements (v{sub 1},…,v{sub l}) of a free metabelian group S of rank r≥2 is primitive if and only if it preserves measure on the variety of metabelian groups A{sup 2}. From this we obtain the result that a system of elements (v{sub 1},…,v{sub l}) is primitive in the group S if and only if it is primitive in its profinite completion S-hat . Furthermore, it is proved that there exist a variety M and a nonprimitive element v∈F{sub r}(M) such that v preserves measure on M. Bibliography: 13 titles.
Authors:
 [1]
  1. Novosibirsk State Technical University, Novosibirsk (Russian Federation)
Publication Date:
OSTI Identifier:
22365853
Resource Type:
Journal Article
Resource Relation:
Journal Name: Sbornik. Mathematics; Journal Volume: 204; Journal Issue: 12; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; GROUP THEORY; MATHEMATICAL MODELS; MATHEMATICAL SOLUTIONS; SYMMETRY GROUPS