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A characterisation of finite soluble groups in which Sylow permutability is a transitive relation by means of subgroup embedding
properties enjoyed by all the subgroups is proved. The key point is an extension of a subnormality criterion due to Wielandt.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
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M. Kuzucuoğlu 《Journal of Mathematical Sciences》2013,195(4):486-486
We study some properties for barely transitive group. 相似文献
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Let G be a finite group. We say that G is a T0-group, if its Frattini quotient group G/F(G)G/\Phi (G) is a T-group, where by a T-group we mean a group in which every subnormal subgroup is normal. We determine the structure of a non T0-group G all of whose proper subgroups are T0-groups. 相似文献
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We classify the groups satisfying the following conditions: i) is locally finite; ii) is a sharply triply transitive permutation group; iii) all elements of have fixpoints.Published in Ukraninskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 1060–1065, July–August, 1991. 相似文献
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Michael Woltermann 《代数通讯》2013,41(17):1877-1883
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M. Ramadan 《Acta Mathematica Hungarica》2007,114(3):187-193
Let G be a finite group. A PT-group is a group G whose subnormal subgroups are all permutable in G. A PST-group is a group G whose subnormal subgroups are all S-permutable in G. We say that G is a PTo-group (respectively, a PSTo-group) if its Frattini quotient group G/Φ(G) is a PT-group (respectively, a PST-group). In this paper, we determine the structure of minimal non-PTo-groups and minimal non-PSTo-groups.
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David Chillag 《Israel Journal of Mathematics》1975,21(1):50-53
LetG be a nonsolvable transitive permutation group of prime degreep. LetP be a Sylow-p-subgroup ofG and letq be a generator of the subgroup ofN G(P) fixing one point. Assume that |N G(P)|=p(p?1) and that there exists an elementj inG such thatj ?1qj=q(p+1)/2. We shall prove that a group that satisfies the above condition must be the symmetric group onp points, andp is of the form 4n+1. 相似文献
10.
A. Ballester-Bolinches L.A. Kurdachenko Tatiana Pedraza 《Journal of Pure and Applied Algebra》2007,210(3):665-671
A group G is said to be a -group if permutability is a transitive relation in the set of all subgroups of G. Our purpose in this paper is to study -groups in the class of periodic radical groups satisfying min-p for all primes p. 相似文献
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D. F. Holt 《Journal of Graph Theory》1981,5(2):201-204
A graph having 27 vertices is described, whose automorphism group is transitive on vertices and undirected edges, but not on directed edges. 相似文献
13.
Pedro Lopes 《Central European Journal of Mathematics》2009,7(4):650-659
In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a
subset of its generators such that these generators alone (the so-called primitive generators) imply the group is primitive.
The remaining generators ensure transitivity or comply with specific features of the group.
We show that, other than the symmetric and alternating groups, there are infinitely many primitive groups with one primitive
generator each. These primitive groups are certain Mathieu groups, certain projective general and projective special linear
groups, and certain subgroups of some affine special linear groups. 相似文献
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Anne Delandtsheer 《Archiv der Mathematik》1986,47(5):395-400
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In this note, we give a complete classification of finite groups in which all noncyclic proper subgroups have the same order. 相似文献
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A subgroup H of a finite group G is called a TI-subgroup if H ∩ H x = 1 or H for any x ∈ G. In this short note, the finite groups all of whose nonabelian subgroups are TI-subgroups are classified. 相似文献
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