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41.
We prove that if a group G is residually
, then for every
-subgroup of the group G, the set of -roots from this subgroup is a -separable
-subgroup. 相似文献
42.
V. V. Bludov 《Algebra and Logic》2003,42(5):304-317
We prove a theorem saying that in finitely generated linearly ordered metabelian groups there exists a finite system of normal convex subgroups satisfying orderability conditions for groups, and an embedding theorem for linearly ordered metabelian groups whose initial linear orders extend to -divisible linearly ordered metabelian ones. As a consequence, it is stated that orderable metabelian groups are embedded, with extension of all their linear orders, in -divisible orderable metabelian groups. 相似文献
43.
A proper subgroup H of a group G is said to be strongly embedded if 2 (H) and 2(HH
g) (for all
). An involution i of G is said to be finite if
(for all g G). As is known, the structure of a (locally) finite group possessing a strongly embedded subgroup is determined by the theorems of Burnside and Brauer--Suzuki, provided that the Sylow 2-subgroup contains a unique involution. In this paper, sufficient conditions for the equality m
2(G)= 1 are established, and two analogs of the Burnside and Brauer—Suzuki theorems for infinite groups G possessing a strongly embedded subgroup and a finite involution are given. 相似文献
44.
The structure of groups in which many subgroups have a certain property X has been investigated for several choices of the property X. Groups whose non-normal subgroups satisfy certain finite rank conditions are studied in this article. In particular, a classification of groups in which every subgroup is either normal or polycyclic is given.(Dedicated to Mario Curzio on the occasion of his 70th birthday)1991 Mathematics Subject Classification: 20F16 相似文献
45.
A. S. Sivatski 《Algebra Colloquium》2000,7(2):197-204
Let A be a commutative ring and n 3 a positive integer. In this paper, we consider unimodular rows (f1(x),..., fn(x)) over A[x]. We prove that, if the row of the leading coefficients of fi(x) is unimodular over A and a A, then there exists En(A[x]) such that (f1(x),...,fn(x)) = (f1(a),...,fn(a)). Also, if A is a Noetherian ring with finite Krull dimension and the row of leading coefficients satisfies the same condition, then we give a bound for the length of in terms of elementary transvections.Partially supported by INTAS 93–436EXT and DFG–RFBR grant No. 96–01–00092G.2000 Mathematics Subject Classification: 19A13, 19B14, 13C10, 13B25, 13F20 相似文献
46.
Eon-Kyung Lee 《代数通讯》2013,41(3):1121-1139
In this article, we show that for every abelian subgroup H of a Garside group, some conjugate g ?1 Hg consists of ultra summit elements and the centralizer of H is a finite index subgroup of the normalizer of H. Combining with the results on translation numbers in Garside groups, we obtain an easy proof of the algebraic flat torus theorem for Garside groups and solve several algorithmic problems concerning abelian subgroups of Garside groups. 相似文献
47.
V. V. Korableva 《Siberian Mathematical Journal》2008,49(2):273-286
We determine the ranks of the permutation representations of the simple groups B l (q), C l (q), and D l (q) on the cosets of the parabolic maximal subgroups. 相似文献
48.
We prove that a group generated by a twisted subset is finite and its order is bounded by some function depending only on the order of the twisted subset. 相似文献
49.
In this paper we have completely determined: (1) all almost simple groups which act 2-transitively on one of their sets of
Sylow p-subgroups. (2) all non-abelian simple groups T whose automorphism group acts 2-transitively on one of the sets of Sylow p-subgroups of T. (3) all finite groups which are 2-transitive on all their sets of Sylow subgroups.
The first author acknowledges the support of OPR Scholarship of Australia
The second author is supported by the National Natural Science Foundation of China. Thanks are also due to the Department
of Mathematics, the University of Western Australia, where he did his part of this work for its hospitality 相似文献
50.
The location of quasinormal subgroups in a group is not particularly well known. Maximal ones always have to be normal, but
little has been proved about the minimal ones. In finite groups, the difficulties arise in the p-groups. Here we prove that, for every odd prime p, a quasinormal subgroup of order p
2 in a finite p-group G contains a quasinormal subgroup of G of order p.
S. Stonehewer is grateful to the Australian National University for financial support during the preparation of this paper. 相似文献