Subnormal and ascendant subgroups with rank restrictions
نویسندگان
چکیده
منابع مشابه
Connected transversals to subnormal subgroups
Subnormal subgroups possessing connected transversals are briefly discussed.
متن کاملFinite Groups Whose «-maximal Subgroups Are Subnormal
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...
متن کاملThe Nilpotency of Some Groups with All Subgroups Subnormal
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.
متن کاملon supersolvability of finite groups with $mathbb p$-subnormal subgroups
in this paper we find systems of subgroups of a finite group, which $bbb p$nobreakdash-hspace{0pt}subnormality guarantees supersolvability of the whole group.
متن کاملA Class of Subnormal Operators with Finite Rank Self-commutators
In this paper, the family of pure subnormal operators S with m.n.e. N and finite rank self-commutators satisfying c~(S) = closed unit disk and or(N) = unit circle U{a l , . . . , am} is studied. A necessary and sufficient condition for a pair of matrices {A, C} to be a complete unitary invariance of S in this family is given. The concrete model for some sub-family of this family is also given i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1990
ISSN: 0019-2082
DOI: 10.1215/ijm/1255988490