منابع مشابه
Connected transversals to subnormal subgroups
Subnormal subgroups possessing connected transversals are briefly discussed.
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Introduction. Dedekind has determined all groups whose subgroups are all normal (see, e.g., [5, Theorem 12.5.4]). Partially generalizing this, Wielandt showed that a finite group is nilpotent, if and only if all its subgroups are subnormal, and also if and only if all maximal subgroups are normal [5, Corollary 10.3.1, 10.3.4]. Huppert [7, Sätze 23, 24] has shown that if all 2nd-maximal subgroup...
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Let G be a group with all subgroups subnormal. A normal subgroup N of G is said to be G-minimax if it has a finite G-invariant series whose factors are abelian and satisfy either max-G or minG. It is proved that if the normal closure of every element of G is G-minimax then G is nilpotent and the normal closure of every element is minimax. Further results of this type are also obtained.
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Let $G$ be a group and $H$ a subgroup of $G$. $H$ is said to have semi-$Pi$-property in $G$ if there is a subgroup $T$ of $G$ such that $G=HT$ and $Hcap T$ has $Pi$-property in $T$. In this paper, investigating on semi-$Pi$-property of subgroups, we shall obtain some new description of finite groups.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1998
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-98-04126-4