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1
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On the structure of groups whose non-abelian subgroups are subnormal

100%
Kurdachenko L., Atlıhan S., Semko N.
Open Mathematics
|
2014
|
tom 12
|
nr 12
1762-1771
EN
The main aim of this article is to examine infinite groups whose non-abelian subgroups are subnormal. In this sense we obtain here description of such locally finite groups and, as a consequence we show several results related to such groups.
2
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On locally finite minimal non-solvable groups

76%
Arıkan A., Sezer S., Smith H.
Open Mathematics
|
2010
|
tom 8
|
nr 2
266-273
EN
In the present work we consider infinite locally finite minimal non-solvable groups, and give certain characterizations. We also define generalizations of the centralizer to establish a result relevant to infinite locally finite minimal non-solvable groups.
3
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Groups with every subgroup ascendant-by-finite

76%
Camp-Mora S.
Open Mathematics
|
2013
|
tom 11
|
nr 12
2182-2185
EN
A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.
4
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Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov

76%
Cutolo G., Smith H.
Open Mathematics
|
2012
|
tom 10
|
nr 3
942-949
EN
Let G be a locally finite group satisfying the condition given in the title and suppose that G is not nilpotent-by-Chernikov. It is shown that G has a section S that is not nilpotent-by-Chernikov, where S is either a p-group or a semi-direct product of the additive group A of a locally finite field F by a subgroup K of the multiplicative group of F, where K acts by multiplication on A and generates F as a ring. Non-(nilpotent-by-Chernikov) extensions of this latter kind exist and are described in detail.
5
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Almost fixed-point-free automorphisms of prime order

76%
Wehrfritz B.
Open Mathematics
|
2011
|
tom 9
|
nr 3
616-626
EN
Let ϕ be an automorphism of prime order p of the group G with C G(ϕ) finite of order n. We prove the following. If G is soluble of finite rank, then G has a nilpotent characteristic subgroup of finite index and class bounded in terms of p only. If G is a group with finite Hirsch number h, then G has a soluble characteristic subgroup of finite index in G with derived length bounded in terms of p and n only and a soluble characteristic subgroup of finite index in G whose index and derived length are bounded in terms of p, n and h only. Here a group has finite Hirsch number if it is poly (cyclic or locally finite). This is a stronger notion than that used in [Wehrfritz B.A.F., Almost fixed-point-free automorphisms of order 2, Rend. Circ. Mat. Palermo (in press)], where the case p = 2 is discussed.
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