Levi quasivarieties of exponent p ^{ s }
 V. V. Lodeishchikova
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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.
 L. C. Kappe, “On Leviformations,” Arch. Math., 23, No. 6, 561–572 (1972). CrossRef
 F. W. Levi, “Groups in which the commutator operation satisfies certain algebraic conditions,” J. Indian Math. Soc., 6, 87–97 (1942).
 R. F. Morse, “Leviproperties generated by varieties,” in Cont. Math., 169, Am. Math. Soc., Providence, RI (1994), pp. 467–474.
 A. I. Budkin, “Levi quasivarieties,” Sib. Mat. Zh., 40, No. 2, 266–270 (1999).
 A. I. Budkin, “Levi classes generated by nilpotent groups,” Algebra Logika, 39, No. 6, 635–647 (2000).
 L. C. Kappe and W. P. Kappe, “On threeEngel groups,” Bull. Austr. Math. Soc., 7, No. 3, 391–405 (1972). CrossRef
 A. I. Budkin and L. V. Taranina, “On Levi quasivarieties generated by nilpotent groups,” Sib. Mat. Zh., 41, No. 2, 270–277 (2000).
 V. V. Lodeishchikova, “On Levi quasivarieties generated by nilpotent groups,” Izv. Altai State Univ., No. 1(61), 26–29 (2009).
 A. I. Budkin and V. A. Gorbunov, “Quasivarieties of algebraic systems,” Algebra Logika, 14, No. 2, 123–142 (1975).
 A. I. Budkin, Quasivarieties of Groups [in Russian], Altai State Univ., Barnaul (2002).
 M. I. Kargapolov and Yu. I. Merzlyakov, Fundamentals of Group Theory [in Russian], Nauka, Moscow (1984).
 A. I. Mal’tsev, Algebraic Systems [in Russian], Nauka, Moscow (1970).
 H. Neumann, Varieties of Groups, Springer, Berlin (1967).
 A. G. Kurosh, Group Theory [in Russian], Nauka, Moscow (1967).
 V. A. Gorbunov, Algebraic Theory of Quasivarieties, Sib. School Alg. Log. [in Russian], Nauch. Kniga, Novosibirsk (1999).
 A. N. Fyodorov, “Quasiidentities of finite 2nilpotent groups,” VINITI, Dep. No. 5489B87 (1987).
 Title
 Levi quasivarieties of exponent p ^{ s }
 Journal

Algebra and Logic
Volume 50, Issue 1 , pp 1728
 Cover Date
 20110301
 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