Levi quasivarieties of exponent p s
- 22 Downloads
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 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.
Keywordsquasivariety Levi classes nilpotent groups
Unable to display preview. Download preview PDF.
- 3.R. F. Morse, “Levi-properties generated by varieties,” in Cont. Math., 169, Am. Math. Soc., Providence, RI (1994), pp. 467–474.Google Scholar
- 8.V. V. Lodeishchikova, “On Levi quasivarieties generated by nilpotent groups,” Izv. Altai State Univ., No. 1(61), 26–29 (2009).Google Scholar
- 10.A. I. Budkin, Quasivarieties of Groups [in Russian], Altai State Univ., Barnaul (2002).Google Scholar
- 11.M. I. Kargapolov and Yu. I. Merzlyakov, Fundamentals of Group Theory [in Russian], Nauka, Moscow (1984).Google Scholar
- 12.A. I. Mal’tsev, Algebraic Systems [in Russian], Nauka, Moscow (1970).Google Scholar
- 14.A. G. Kurosh, Group Theory [in Russian], Nauka, Moscow (1967).Google Scholar
- 15.V. A. Gorbunov, Algebraic Theory of Quasivarieties, Sib. School Alg. Log. [in Russian], Nauch. Kniga, Novosibirsk (1999).Google Scholar
- 16.A. N. Fyodorov, “Quasi-identities of finite 2-nilpotent groups,” VINITI, Dep. No. 5489-B87 (1987).Google Scholar