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Groups with small deviation for non-subnormal subgroups

100%
Kurdachenko L., Smith H.
Open Mathematics
|
2009
|
tom 7
|
nr 2
186-199
EN
We introduce the notion of the non-subnormal deviation of a group G. If the deviation is 0 then G satisfies the minimal condition for nonsubnormal subgroups, while if the deviation is at most 1 then G satisfies the so-called weak minimal condition for such subgroups (though the converse does not hold). Here we present some results on groups G that are either soluble or locally nilpotent and that have deviation at most 1. For example, a torsion-free locally nilpotent with deviation at most 1 is nilpotent, while a Baer group with deviation at most 1 has all of its subgroups subnormal.
2
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Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov

100%
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.
3
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On locally finite minimal non-solvable groups

81%
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.
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