Metabelian Pro-p-Groups with a Single Relation

Metabelian Pro-p-Groups with a Single Relation

It is proved that there exist uncountably many nonisomorphic pro-p-groups admitting presentations with two generating elements and one defining relation in the variety of metabelian pro-p-groups. Also we give information on pro-p-groups with a single relation in varieties of nilpotent pro-p-groups.

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Veröffentlicht in:Algebra and logic 2020-03, Vol.59 (1), p.82-86
1. Verfasser: Romanovskii, N. S.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Isomorphisms (Mathematics)
Mathematical Logic and Foundations
Mathematical research
Mathematics
Mathematics and Statistics
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Zusammenfassung:It is proved that there exist uncountably many nonisomorphic pro-p-groups admitting presentations with two generating elements and one defining relation in the variety of metabelian pro-p-groups. Also we give information on pro-p-groups with a single relation in varieties of nilpotent pro-p-groups.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-020-09580-1