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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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Annalisa Galoppo 《Rendiconti del Circolo Matematico di Palermo》1998,47(3):397-408
In this paper groups in which the set Σ of the normal or self-normalizing subgroups is large will be studied. In particular
it will be characterized locally graded groups satisfying the minimal condition on subgroups which do not belong to Σ and
locally finite groups for which the set Σ is dense in the lattice of all subgroups. 相似文献
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Annalisa Galoppo 《Rendiconti del Circolo Matematico di Palermo》1923,47(3):397-408
In this paper groups in which the set Σ of the normal or self-normalizing subgroups is large will be studied. In particular it will be characterized locally graded groups satisfying the minimal condition on subgroups which do not belong to Σ and locally finite groups for which the set Σ is dense in the lattice of all subgroups. 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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It is a theorem of Shor that ifG is a word-hyperbolic group, then up to isomrphism, only finitely many groups appear as fixed subgroups of automorphisms ofG. We give an example of a groupG acting freely and cocompactly on a CAT(0) square complex such that infinitely many non-isomorphic groups appear as fixed
subgroups of automorphisms ofG. Consequently, Shor’s finiteness result does not hold if the negative curvature condition is relaxed to either biautomaticity
or nonpositive curvature.
D. T. Wise was supported by grants from FCAR and NSERC. 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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Maria De Falco Francesco de Giovanni 《Bulletin of the Brazilian Mathematical Society》2000,31(1):73-80
A group is said to be aT-group if all its subnormal subgroups are normal. The structure of groups satisfying the minimal condition on subgroups that do not have the propertyT is investigated. Moreover, locally soluble groups with finitely many conjugacy classes of subgroups which are notT-groups are characterized. 相似文献
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Aziza Rezig 《代数通讯》2018,46(3):1344-1352
A group is called (PF)L if the subgroups generated by its elements having same order (finite or infinite) are polycyclic-by-finite. In the present paper we prove that a group is locally graded minimal non-((PF)L∪(𝔓𝔉)𝔄) if, and only if, it is non-perfect minimal non-FC, where (𝔓𝔉)𝔄 denotes the class of (polycyclic-by-finite)-by-abelian groups. We prove also that a group of infinite rank whose proper subgroups of infinite rank are in ((PF)L∪(𝔓𝔉)𝔄) is itself in ((PF)L∪(𝔓𝔉)𝔄) provided that it is locally (soluble-by-finite) without simple homomorphic images of infinite rank. Our last result concerns groups that satisfy the minimal condition on non-((PF)L∪(𝔓𝔉)𝔄)-subgroups. 相似文献
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Enrico Jabara 《Czechoslovak Mathematical Journal》2018,68(2):491-496
A group G has all of its subgroups normal-by-finite if H/H G is finite for all subgroups H of G. The Tarski-groups provide examples of p-groups (p a “large” prime) of nonlocally finite groups in which every subgroup is normal-by-finite. The aim of this paper is to prove that a 2-group with every subgroup normal-by-finite is locally finite. We also prove that if |H/H G | 6 2 for every subgroup H of G, then G contains an Abelian subgroup of index at most 8. 相似文献
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Groups with maximal subgroups of Sylow subgroups normal 总被引:3,自引:0,他引:3
Gary L. Walls 《Israel Journal of Mathematics》1982,43(2):166-168
This paper characterizes those finite groups with the property that maximal subgroups of Sylow subgroups are normal. They
are all certain extensions of nilpotent groups by cyclic groups. 相似文献
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Avino’am Mann 《Israel Journal of Mathematics》1968,6(1):13-25
A group is said to have dense normal subgroups, if each non-empty open interval in its lattice of subgroups contains a normal
subgroup. The structure of this and related classes of groups is investigated. Typical results are: an infinite group with
dense ascendant subgroups is locally nilpotent: a nontorsion group with dense normal subgroups is abelian, etc. 相似文献
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 3, pp. 323–327, March, 1989. 相似文献
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Maurizio Valsecchi 《Rendiconti del Circolo Matematico di Palermo》1929,53(1):129-152
We give the structure of finite groups belonging to some families defined by conditions of complementation. 相似文献
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