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1
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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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The rank of the factor-group modulo the hypercenter and the rank of the some hypocenter of a group

100%
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.
3
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On some infinite dimensional linear groups

81%
Kurdachenko L., Sadovnichenko A., Subbotin I.
Open Mathematics
|
2009
|
tom 7
|
nr 2
176-185
EN
Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dimF(B/CoreG(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.
4
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On some properties of pronormal subgroups

81%
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.
5
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Infinite dimensional linear groups with many G - invariant subspaces

81%
Kurdachenko L., Sadovnichenko A., Subbotin I.
Open Mathematics
|
2010
|
tom 8
|
nr 2
261-265
EN
Let F be a field, A be a vector space over F, GL(F, A) be the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dim F(B/Core G(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char F.
6
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Groups whose all subgroups are ascendant or self-normalizing

81%
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].
7
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On the structure of groups whose non-abelian subgroups are subnormal

81%
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.
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