منابع مشابه
Math 5520 Class Notes Commutators, Solvable and Nilpotent Groups
A group is simple if it has no non-trivial, proper, normal subgroups. It’s not hard to show that if n > 4, then An is a simple group. Recall that for a field F , SLn(F ) is the subgroup of GLn(F ) consisting of matrices with determinant 1. Define PSLn(F ) = SLn(F )/Z(SLn(F )). Here, S is for “special” and P is for “projective.” It can be shown that PSLn(F ) is simple for all n and F except for ...
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In this paper we will prove analogues of B. Maier’s characterization of weak and strong embeddability of amalgams in N2 [12, 13] for the subvarieties of N2. We will also give analogues of D. Saracino’s characterization of weak and strong amalgamation bases [17], the author’s work on dominions [11] and on amalgamation bases in some varieties of nil-2 groups [8, 9]. Definitions will be recalled b...
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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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We characterize co-Hopfian finitely generated torsion free nilpotent groups in terms of their Lie algebra automorphisms, and construct many examples of such groups.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1952
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1952-0049889-9