Algebra and Logic

, Volume 50, Issue 1, pp 17–28

Levi quasivarieties of exponent ps

Authors

Article

DOI: 10.1007/s10469-011-9121-1

Cite this article as:
Lodeishchikova, V.V. Algebra Logic (2011) 50: 17. doi:10.1007/s10469-011-9121-1
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For 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 ps, 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 2n, with commutator subgroups of exponent 2. Assume also that for all groups in K, elements of order 2m, 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 2n, with commutator subgroups of exponent 2.

Keywords

quasivarietyLevi classesnilpotent groups

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© Springer Science+Business Media, Inc. 2011