SOME INEQUALITIES FOR POLYNILPOTENT MULTIPLIER OF POWERFULL p-GROUPS

Document Type : Original Manuscript

Author

Department of Mathematics, University of Golestan, P.O. Box ,155 Gorgan, Iran.

Abstract

In this paper we present some inequalities for the order, the exponent, and the number of generators of the polynilpotent multiplier, the Baer invariant with respect to the variety of polynilpotent groups of class row (c_1; · · · ; c_t) of a powerful p-group.Our results extend some of Mashakekhy and Maohammadzadeh’s in 2007 to polynilpotent multipliers.

Keywords


1. A. J. Bayes, J. Kautsky and J. W. Wamsley, Computation in Nilpotent Groups (application), in : Lecture Notes in Math. 372, Springer-Verlag (1973) 82–89.
2. J. Burns and G. Ellis, On the Nilpotent multipliers of a group, Math. Z., 226 (1997), 405–423.
3. G. Ellis, On the relation between upper central quotients and lower central series of a group, Trans. Amer. Soc., 353 (2001), 4219–4234.
4. M. Hall, The Theory of Groups, MacMillan Company, NewYork, 1959.
5. N. S. Hekster, Varieties of groups and isologisms, J. Austral. Math. Soc., (series A) 46(1) (1989), 22–60.
6. M. R. Jones, Some inequalities for the multiplicator of a finite group, Proc. Amer. Math. Soc., 39 (1973), 450–456.
7. S. Kayvanfar and M. A. Sanati, A bound for the exponent of the Schur multiplier of a some finite p-group, Bull. Iran. Math. Soc., 26(2) (2000), 89–95.
8. A. Lubotzky and A. Mann, Powerful p-groups. I. finite groups, J. Algebra, 105
(1987), 484–505.
9. B. Mashayekhy and M. Parvizi, Polynilpotent multiplier of finitely generated abelian groups, Int. J. Math., Game Theory and Algebra, 16(2) (2006), 93–102.
10. B. Mashayekhy and F. Mohammadzadeh, Some inequalities for nilpotent multipliers of poweful p-groups, Bull. Iran. Math. Soc., 33(2) (2007), 61–71.
11. M. R. R. Moghaddam, Calculation of the Baer invariant of certain groups, Mh. Math., 97 (1984), 191–206.
12. P. Moravec, Schur multipliers and power endomorphisms of groups, J. Algebra,
308 (2007), 12–25.