, Volume 50, Issue 1, pp 1728
Levi quasivarieties of exponent p ^{ s }
 V. V. LodeishchikovaAffiliated withul. Georgieva 46 Email author
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Get AccessFor an arbitrary class M of groups, L(M) denotes a class of all groups G the normal closure of any element in which belongs to M; qM is a quasivariety generated by M. Fix a prime p, p ≠ 2, and a natural number s, s ≥ 2. Let qF be a quasivariety generated by a relatively free group in a class of nilpotent groups of class at most 2 and exponent p ^{ s }, with commutator subgroups of exponent p. We give a description of a Levi class generated by qF. Fix a natural number n, n ≥ 2. Let K be an arbitrary class of nilpotent groups of class at most 2 and exponent 2^{ n }, with commutator subgroups of exponent 2. Assume also that for all groups in K, elements of order 2^{ m }, 0 < m < n, are contained in the center of a given group. It is proved that a Levi class generated by a quasivariety qK coincides with a variety of nilpotent groups of class at most 2 and exponent 2^{ n }, with commutator subgroups of exponent 2.
Keywords
quasivariety Levi classes nilpotent groups Title
 Levi quasivarieties of exponent p ^{ s }
 Journal

Algebra and Logic
Volume 50, Issue 1 , pp 1728
 Cover Date
 201103
 DOI
 10.1007/s1046901191211
 Print ISSN
 00025232
 Online ISSN
 15738302
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 quasivariety
 Levi classes
 nilpotent groups
 Authors

 V. V. Lodeishchikova ^{(1)}
 Author Affiliations

 1. ul. Georgieva 46, Barnaul, 656057, Russia