On Hall subnormally embedded and generalized nilpotent groups
نویسندگان
چکیده
منابع مشابه
On Torsion-by-Nilpotent Groups
Let C be a class of groups, closed under taking subgroups and quotients. We prove that if all metabelian groups of C are torsion-by-nilpotent, then all soluble groups of C are torsion-by-nilpotent. From that, we deduce the following consequence, similar to a well-known result of P. Hall: if H is a normal subgroup of a group G such that H and G/H ′ are (locally finite)-by-nilpotent, then G is (l...
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The articles [2], [3], [4], [6], [7], [5], [8], [9], [10], and [1] provide the notation and terminology for this paper. For simplicity, we use the following convention: x is a set, G is a group, A, B, H, H1, H2 are subgroups of G, a, b, c are elements of G, F is a finite sequence of elements of the carrier of G, and i, j are elements of N. One can prove the following propositions: (1) ab = a · ...
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Let γi(G) and Zi(G) denote the i-th terms of the lower and upper central series of a group G, respectively. In 1956 P. Hall showed that if γi+1(G) is finite, then the index |G : Z2i(G)| is finite. We prove that the same result holds under the weaker hypothesis that |γi+1(G) : γi+1(G) ∩ Zi(G)| is finite.
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We give a new framework for the construction of homogeneous nilpotent groups and rings which goes a long way toward unifying the two cases, and enables us to extend previous constructions, producing a variety of new examples. In particular we find ingredients for the manufacture of 2No homogeneous nilpotent groups "in nature".
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2013
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2013.04.025