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For a family of group words w we show that if G is a profinite group in which all w-values are contained in a union of finitely many subgroups with a prescribed property, then the verbal subgroup w(G) has the same property as well. In particular, we show this in the case where the subgroups are periodic or of finite rank. If G contains finitely many subgroups G 1, G 2, . . . , G s of finite exponent e whose union contains all γ k -values in G, it is shown that γ k (G) has finite (e, k, s)-bounded exponent. If G contains finitely many subgroups G 1, G 2, . . . , G s of finite rank r whose union contains all γ k -values, it is shown that γ k (G) has finite (k, r, s)-bounded rank. 相似文献
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N. S. Chernikov 《Ukrainian Mathematical Journal》2000,52(3):457-463
We establish results concerning the almost solvability and other properties of groups factorized by two subgroups with finite
or Chernikov commutants. 相似文献
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We consider an almost hyper-Abellan group G of a finite Abelian sectional rank that is the product of two subgroups A and B. We prove that every subgroup H that belongs to the intersection A ∩ B and is ascending both in A and B is also an ascending subgroup in the group G. We also show that, in the general case, this statement is not true.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 6, pp. 842–848, June, 1997. 相似文献
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N. Yu. Verpatova 《Ukrainian Mathematical Journal》1997,49(8):1150-1157
We generalize the well-known nition of complementability of subgroups. We describe the structure of nondispersible generalized
factorized groups all subgroups of which are dispersible.
Ukrainian Pedagogical University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 8, pp. 1025–1031,
August. 1997. 相似文献
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A group is called metahamiltonian if all its non-abelian subgroups are normal; it is known that locally soluble metahamiltonian groups have finite derived
subgroup. This result is generalized here, by proving that every locally graded group with finitely many derived subgroups
of non-normal subgroups has finite derived subgroup. Moreover, locally graded groups having only finitely many derived subgroups
of infinite non-normal subgroups are completely described.
Received: 25 April 2005 相似文献
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Silvana Franciosi Francesco de Giovanni Leonid A. Kurdachenko 《Annali di Matematica Pura ed Applicata》1995,169(1):35-65
Summary An anti-FC-group is a group in which every subgroup either is finitely generated or has only a finite number of coniugates. In this article a classification is given of (generalized) soluble anti-FC-groups which neither are central-by-finite nor satisfy the maximal condition on subgroups. Moreover, groups in which every non-cyclic subgroup has only a finite number of coniugates are characterized. 相似文献
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The solubility of a finite group with less than 6 non-supersoluble subgroups is confirmed in the paper. Moreover we prove that a finite insoluble group has exactly 6 non-supersoluble subgroups if and only if it is isomorphic to \(A_5\) or \({{\mathrm{SL}}}_2(5)\). Furthermore, it is shown that a finite insoluble group has exactly 22 non-nilpotent subgroups if and only if it is isomorphic to \(A_5\) or \({{\mathrm{SL}}}_2(5)\). This confirms a conjecture of Zarrin (Arch Math (Basel) 99:201–206, 2012). 相似文献
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Denote by $\mathfrak{M}$ the set whose elements are the simple 3-dimensional unitary groups U 3(q) and the linear groups L 3(q) over finite fields. We prove that every periodic group, saturated by the groups of a finite subset of $\mathfrak{M}$ , is finite. 相似文献
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Maria De Falco Francesco de Giovanni Carmela Musella 《Rendiconti del Circolo Matematico di Palermo》2010,59(2):289-294
A theorem of Polovickiĭ states that any group with finitely many normalizers of subgroups is finite over its centre. Here
we prove that the centre of a non-periodic group G has finite index if and only if G has finitely many normalizers of non-periodic subgroups. 相似文献
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Abstract A group is called metahamiltonian if all its non-abelian subgroups are normal; it is known that locally soluble metahamiltonian
groups have finite commutator subgroup. Here the structure of locally graded groups with finitely many normalizers of (infinite)
non-abelian subgroups is investigated, and the above result is extended to this more general situation.
Keywords: normalizer subgroup, metahamiltonian group
Mathematics Subject Classification (2000): 20F24 相似文献
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