Determination of all the prime power groups containing only one invariant subgroup of every index which exceeds this prime number
نویسندگان
چکیده
منابع مشابه
Every Odd Perfect Number Has a Prime Factor Which Exceeds
It is proved here that every odd perfect number is divisible by a prime greater than 106.
متن کاملEvery odd perfect number has a prime factor which exceeds 106
It is proved here that every odd perfect number is divisible by a prime greater than 106.
متن کاملGroups in which every subgroup has finite index in its Frattini closure
In 1970, Menegazzo [Gruppi nei quali ogni sottogruppo e intersezione di sottogruppi massimali, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 48 (1970), 559--562.] gave a complete description of the structure of soluble $IM$-groups, i.e., groups in which every subgroup can be obtained as intersection of maximal subgroups. A group $G$ is said to have the $FM$...
متن کاملFinite groups with $X$-quasipermutable subgroups of prime power order
Let $H$, $L$ and $X$ be subgroups of a finite group$G$. Then $H$ is said to be $X$-permutable with $L$ if for some$xin X$ we have $AL^{x}=L^{x}A$. We say that $H$ is emph{$X$-quasipermutable } (emph{$X_{S}$-quasipermutable}, respectively) in $G$ provided $G$ has a subgroup$B$ such that $G=N_{G}(H)B$ and $H$ $X$-permutes with $B$ and with all subgroups (with all Sylowsubgroups, respectively) $...
متن کاملOn the Invariant Subgroups of Prime Index*
The totality formed by all the operators of any group (G) which are common to all the invariant subgroups of prime index (p) constitutes a characteristic subgroup, and the corresponding quotient group is the abelian group of order pK and of type (1, 1, 1, ■■■)-\ The number of the invariant subgroups of index p is therefore pK — 1/p — 1. The given totality includes all the operators of G which a...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1924
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1924-1501288-3