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We describe (generalized) soluble-by-finite groups in which the set of non-normal subgroups which are not finitely generated satisfies the maximal condition. 相似文献
44.
Locally almost solvable groups with a dense system of infinite almost normal subgroups are described in a constructive manner.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, Nos. 7 and 8, pp. 969–973, July–August, 1991. 相似文献
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47.
Leonid A. Kurdachenko Alexsandr A. Pypka Igor Ya. Subbotin 《Central European Journal of Mathematics》2010,8(5):840-845
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. 相似文献
48.
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.
相似文献
49.
Let G be a group with the property that there are no infinite descending chains of non-subnormal subgroups of G for which all successive indices are infinite. The main results are as follows. If G is locally nilpotent then either G is minimax or G has all subgroups subnormal; if G is a Baer group then all subgroups of G are subnormal. It is also proved that a generalised radical group with this property is soluble-by-finite and either is minimax or has all subgroups subnormal. 相似文献
50.
Leonid A. Kurdachenko Alexey V. Sadovnichenko Igor Ya. Subbotin 《Central European Journal of Mathematics》2009,7(2):176-185
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 dim
F
(BFG/B) is finite. A subspace B is called almost G-invariant, if dim
F
(B/Core
G
(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.
相似文献