LOCALLY FINITE GROUPS WHOSE SUBGROUPS HAVE FINITE NORMAL OSCILLATION
نویسندگان
چکیده
منابع مشابه
Classifying fuzzy normal subgroups of finite groups
In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.
متن کاملfinite groups whose minimal subgroups are weakly h*-subgroups
let $g$ be a finite group. a subgroup $h$ of $g$ is called an $mathcal h $ -subgroup in $g$ if $n_g (h)cap h^gleq h$ for all $gin g$. a subgroup $h$ of $g$ is called a weakly $mathcal h^ast $-subgroup in $g$ if there exists a subgroup $k$ of $g$ such that $g=hk$ and $hcap k$ is an $mathcal h$-subgroup in $g$. we investigate the structure of the finite group $g$ under the assump...
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 کاملOn non-normal non-abelian subgroups of finite groups
In this paper we prove that a finite group $G$ having at most three conjugacy classes of non-normal non-abelian proper subgroups is always solvable except for $Gcong{rm{A_5}}$, which extends Theorem 3.3 in [Some sufficient conditions on the number of non-abelian subgroups of a finite group to be solvable, Acta Math. Sinica (English Series) 27 (2011) 891--896.]. Moreover, we s...
متن کاملON p-NILPOTENCY OF FINITE GROUPS WITH SS-NORMAL SUBGROUPS
Abstract. A subgroup H of a group G is said to be SS-embedded in G if there exists a normal subgroup T of G such that HT is subnormal in G and H T H sG , where H sG is the maximal s- permutable subgroup of G contained in H. We say that a subgroup H is an SS-normal subgroup in G if there exists a normal subgroup T of G such that G = HT and H T H SS , where H SS is an SS-embedded subgroup of ...
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: Bulletin of the Australian Mathematical Society
سال: 2013
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s000497271300097x