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1
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Groups whose all subgroups are ascendant or self-normalizing

100%
Kurdachenko L., Otal J., Russo A., Vincenzi G.
Open Mathematics
|
2011
|
tom 9
|
nr 2
420-432
EN
This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups, Math. Z., 1972, 125(1), 1–16].
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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The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group

76%
Kurdachenko L., Otal J.
Open Mathematics
|
2013
|
tom 11
|
nr 10
1732-1741
EN
We compare the special rank of the factors of the upper central series and terms of the lower central series of a group. As a consequence we are able to show some generalizations of a theorem of Reinhold Baer.
4
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On some properties of pronormal subgroups

64%
Kurdachenko L., Pypka A., Subbotin I.
Open Mathematics
|
2010
|
tom 8
|
nr 5
840-845
EN
New results on tight connections among pronormal, abnormal and contranormal subgroups of a group have been established. In particular, new characteristics of pronormal and abnormal subgroups have been obtained.
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