Results 1 to 10 of about 22,060 (219)
Locally Finite Groups and a Theorem of Belyaev [PDF]
Advances in Group Theory and Applications, 2023 We prove that a locally finite group satisfying the minimal condition on 2-subgroups is (locally soluble)-by-(quasi linear)-by-abelian-by-finite. Belyaev’s theorem, that a locally finite group satisfying the minimal condition on p-subgroups for every ...
B.A.F. Wehrfritz
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Characterising Locally Finite Groups Satisfying the Strong Sylow Theorem for the Prime p [PDF]
Advances in Group Theory and Applications, 2022 During his lectures to the 1987 Singapore Group Theory Conference Otto H. Kegel proposed the following question: “If every subgroup S of the locally finite group G contains a finite p-subgroup which is singular in S, does G then satisfy the strong Sylow ...
Felix F. Flemisch
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Groups with Finitely Many Isomorphism Classes of Non-Normal Subgroups [PDF]
Advances in Group Theory and Applications, 2020 We study groups in which the non-normal subgroups fall into finitely many isomorphism classes. We prove that a locally generalized radical group with this property is abelian-by-finite and minimax.
Leonid A. Kurdachenko +2 more
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Infinite locally finite simple groups with many complemented subgroups [PDF]
International Journal of Group Theory, 2022 We prove that the following families of (infinite) groups have complemented subgroup lattice: alternating groups, finitary symmetric groups, Suzuki groups over an infinite locally finite field of characteristic $2$, Ree groups over an infinite ...
Maria Ferrara, Marco Trombetti
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On infinite groups whose finite quotients have restricted prime divisors [PDF]
International Journal of Group Theory, 2021 The effect of restricting the set of primes dividing the orders of the finite quotients of a group is investigated. Particular attention is paid to abelian, soluble, locally soluble and locally finite groups.
Derek J. S. Robinson
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Groups in which all Subgroups are Subnormal-by-Finite [PDF]
Advances in Group Theory and Applications, 2016 We prove that a locally finite group G in which every subgroup is a finite extension of a subnormal subgroup of G is nilpotent-by-\v Cernikov.
Carlo Casolo
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On Periodic Groups Saturated with Finite Frobenius Groups
Известия Иркутского государственного университета: Серия "Математика", 2021 A group is called weakly conjugate biprimitively finite if each its element of prime order generates a finite subgroup with any of its conjugate elements. A binary finite group is a periodic group in which any two elements generate a finite subgroup. If $
B. E. Durakov, A.I. Sozutov
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Groups Factorized by Pairwise Permutable Abelian Subgroups of Finite Rank [PDF]
Advances in Group Theory and Applications, 2016 It is proved that a group which is the product of pairwise permutable abelian subgroups of finite Prüfer rank is hyperabelian with finite Prüfer rank; in the periodic case the Sylow subgroups of such a product are described.
Bernhard Amberg, Yaroslav P. Sysak
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Locally Finite Groups Saturated with Direct Product of Two Finite Dihedral Groups
Известия Иркутского государственного университета: Серия "Математика", 2023 In the study of infinite groups, as a rule, some finiteness conditions are imposed. For example, the group is required to be periodic, Shunkov group, Frobenius group, locally finite group.
A. V. Kukharev, A.A. Shlepkin
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LATTICE UNIVERSALITY OF LOCALLY FINITE \(p\)-GROUPS
Ural Mathematical Journal, 2023 For an arbitrary prime \(p\), we prove that every algebraic lattice is isomorphic to a complete sublattice in the subgroup lattice of a suitable locally finite \(p\)-group.
Vladimir B. Repnitskiǐ
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