Results 11 to 20 of about 23,113 (304)
LATTICE UNIVERSALITY OF LOCALLY FINITE \(p\)-GROUPS [PDF]
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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On Centralizers in Locally Finite Groups
Journal of Algebra, 2001 We give a flavour of this paper by quoting a couple of its results. Let \(G\) be a locally finite group containing a finite \(p\)-subgroup \(A\) such that \(C_G(A)\) is finite and a non-cyclic subgroup \(B\) of order \(p^2\) such that \(C_G(b)\) has finite exponent for each non-trivial element \(b\) of \(B\).
Shumyatsky, Pavel, Pavel Shumyatsky
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On some generalization of pronormal subgroups in locally finite group
Vìsnik Dnìpropetrovsʹkogo Unìversitetu: Serìâ Matematika, 2015 We proved that if every subgroup of locally finite group is monopronormal, then this group is a $\overline{T}$-group.
A.A. Pypka, N.A. Turbay
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On Direct Products of Dihedral Groups in Locally Finite Groups
Известия Иркутского государственного университета: Серия "Математика"When studying infinite groups, as a rule, some finiteness conditions are imposed. For example, they require that the group be periodic, a Shunkov group, a Frobenius group, or a locally finite group.
I. A. Timofeenko, A.A. Shlepkin
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An example of a non-Borel locally-connected finite-dimensional topological group
Karpatsʹkì Matematičnì Publìkacìï, 2017 According to a classical theorem of Gleason and Montgomery, every finite-dimensional locally path-connected topological group is a Lie group. In the paper for every $n\ge 2$ we construct a locally connected subgroup $G\subset{\mathbb R}^{n+1}$ of ...
I.Ya. Banakh, T.O. Banakh, M.I. Vovk
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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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Characteristic subgroups in locally finite groups
Journal of Algebra, 2012 If a group \(G\) possesses a subgroup \(T\) of finite index, it possesses also a proper normal subgroup of finite index. The authors want instead a characteristic subgroup \(U\), they restrict themselves to locally finite groups \(G\) and subgroups \(T\) with a finite normal series with quotients that are locally nilpotent or satisfy given outer ...
Makarenko, N.Yu., Shumyatsky, P.
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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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