Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/111585
Title: The Strict Upper Bound of Ranks of Commutator Subgroups of Finite p-groups
Other Titles: Точная верхняя граница рангов коммутантов конечных p-групп
Authors: Veretennikov, B. M.
Issue Date: 2019
Publisher: Sobolev Institute of Mathematics
Sobolev Institute of Mathematics
Citation: Veretennikov B. M. Точная верхняя граница рангов коммутантов конечных p-групп [The Strict Upper Bound of Ranks of Commutator Subgroups of Finite p-groups] / B. M. Veretennikov // Siberian Electronic Mathematical Reports. — 2019. — Vol. 16. — P. 1885-1900.
Abstract: All groups in the abstract are finite. We define rank d (G) of a p-group G as the minimal number of generators of G. Let p be any prime number, k1, …, kn – positive integers, n ≥ 2. By D(k1, …, kn) we denote the number of sequences i1, …, ikin which k > 2, i1, …, ik are positive integers from [1, n], ii > i2, i2 ≤ … ≤ ikand for any j Є [1, n] number j may not occur in such sequences more than [figure presented] times. We prove that for any p-group G generated by elements a1, …, an of orders [figure presented](n > 2) the inequality d(G‘) < D(k1, …, kn, p) is true and the equality in this inequality is attainable. Also, we prove that for any p-group G generated by elements a1, …, an of orders [figure presented] (n ≥ 2), with elementary abelian commutator subgroup G’ the class of nilpotency of G’ does not exceed [figure presented]n and this upper bound is also attainable. © 2019 bepetehhnkob b.m.
Keywords: DEFINITION OF A GROUP BY MEANS OF GENERATORS AND DEFINING RELATIONS
FINITE P-GROUP GENERATED BY ELEMENTS OF ORDERS NUMBER OF GENERATORS OF COMMUTATOR SUBGROUP OF A FINITE P-GROUP
THE CLASS OF NILPOTENCY OF OF A FINITE P-GROUP WITH ELEMENTARY ABELIAN COMMUTATOR SUBGROUP
URI: http://hdl.handle.net/10995/111585
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85125195605
PURE ID: 11782787
ISSN: 1813-3304
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

Files in This Item:
File Description SizeFormat 
2-s2.0-85125195605.pdf225,5 kBAdobe PDFView/Open


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.