Subnormal structure of finite soluble groups
نویسندگان
چکیده
منابع مشابه
Finite subnormal coverings of certain solvable groups
A group is said to have a finite covering by subgroups if it is the set theoretic union of finitely many subgroups. A theorem of B. H. Neumann [11] characterizes groups with finite coverings by proper subgroups as precisely those groups with finite non-cyclic homomorphic images. R. Baer (see [13, Theorem 4.16]) proved that a group has a finite covering by abelian subgroups if and only if it is ...
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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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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2002
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700020797