سال انتشار: ۱۳۸۶
محل انتشار: سی و هشتمین کنفرانس ریاضی ایران
تعداد صفحات: ۳
MAHBOOBEH ALIZADEH SANATI – Department of Sciences, Golestan University, Department of Mathematics, Ferdowsi University of mashhad.
BEHROOZ MASHAYEKHY –
Let Nc1, …., ct be the variety of polynilpotent groups of class row (c1, …, ct) It this paper, first, we show that a polynilpotent group G of class row (c1, …, ct) has no any Nc1, …, ct, ct+1 -covering group if this Baer-invariant with pespect to the variety Nc1, …, ct,ct+1 is nontrivial. As an immediate consequence, we can conclude that a solvable group G of length c with nontrivial solvable multiplier, SnM (G), has no Sn-convering group for all n>c, where Sn is the variety of solvable groups of length at most n. Second, we prove that if G is a polynilpotent group of class row (c1, …, ct,ct+1) such that Nc′۱, …, c′t, c′t+1 M(G) ≠۱, where c′i ≥ci for all 1≤ i ≤ t and c′t+1 > ct+1, then G has no any Nc′۱, …, c′t, c′t+1 -covering group.