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A. A. Trofimuk 《Mathematical Notes》2010,87(1-2):264-270
The dependence of the derived length of a finite solvable group on the orders of nonbicyclic Sylow subgroups of the Fitting subgroup is established. 相似文献
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Siberian Mathematical Journal - Let $ G $ be a group. A subgroup $ H $ is weakly subnormal in $ G $ if $ H=\langle A,B\rangle $ for some subnormal subgroup $ A $ and... 相似文献
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Mathematical Notes - In the paper, a characterization is obtained for a finite group such that, for each prime p, every maximal subgroup of any Sylow p-subgroup of this group is contained in a... 相似文献
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We establish the dependence of the derived length and p-length of a finite soluble group on its rank. 相似文献
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Algebra and Logic - A subgroup A is seminormal in a finite group G if there exists a subgroup B such that G = AB and AX is a subgroup for each subgroup X from B. We study a group G = G1G2 . . .Gn... 相似文献
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Let P be a subgroup of a Sylow subgroup of a finite group G. If P is a Sylow subgroup of some normal subgroup of G then P is called normally embedded in G. We establish tests for a finite group G to be p-supersoluble provided that every maximal subgroup of a Sylow p-subgroup of X is normally embedded in G. We study the cases when X is a normal subgroup of G, X = Op',p(H), and X = F*(H) where H is a normal subgroup of G. 相似文献
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All groups considered in this paper will be finite. Our main result here is the following theorem. Let G be a solvable group in which the Sylow p-subgroups are either bicyclic or of order p
3 for any p ∈ π(G). Then the derived length of G is at most 6. In particular, if G is an A4-free group, then the following statements are true: (1) G is a dispersive group; (2) if no prime q ∈ π(G) divides p
2 + p + 1 for any prime p ∈ π(G), then G is Ore dispersive; (3) the derived length of G is at most 4. 相似文献
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