منابع مشابه
On the Structure of Certain Factorizable Groups. Ii
1. In [3], we have shown that in a finite ZP-group G in which A and B are cyclic and A is its own normalizer, the commutator subgroup T of G is cyclic and G = AT with AC\T= I. This result can be used to determine the structure of arbitrary ZP-groups in which A and B are cyclic. If A is a subgroup of a group G, define the subgroup Ni(A) of G inductively by the formula Ni(A)=No(Ni~1(A)), and deno...
متن کاملOn the Structure of Certain Factorizable Groups, I
1. A considerable amount is known about the structure of finite factorizable groups—that is, groups G which can be represented in the form AB, where A and B are subgroups of G. Such groups are known to be solvable under a variety of assumptions on the subgroups A and B. If A and B are both Abelian, Ito [6] has shown that G is actually metabelian. If A and B are both cyclic, it is easy to see th...
متن کاملON THE CHARACTERISTIC DEGREE OF FINITE GROUPS
In this article we introduce and study the concept of characteristic degree of a subgroup in a finite group. We define the characteristic degree of a subgroup H in a finite group G as the ratio of the number of all pairs (h,α) ∈ H×Aut(G) such that h^α∈H, by the order of H × Aut(G), where Aut(G) is the automorphisms group of G. This quantity measures the probability that H can be characteristic ...
متن کاملon finite arithmetic groups
let $f$ be a finite extension of $bbb q$, ${bbb q}_p$ or a global field of positive characteristic, and let $e/f$ be a galois extension. we study the realization fields of finite subgroups $g$ of $gl_n(e)$ stable under the natural operation of the galois group of $e/f$. though for sufficiently large $n$ and a fixed algebraic number field $f$ every its finite extension $e$ is re...
متن کاملon finite c-tidy groups
a group $g$ is said to be a c-tidy group if for every element $x in g setminus k(g)$, the set $cyc(x)=lbrace y in g mid langle x, y rangle ; {rm is ; cyclic} rbrace$ is a cyclic subgroup of $g$, where $k(g)=underset{x in g}bigcap cyc(x)$. in this short note we determine the structure of finite c-tidy groups.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1984
ISSN: 0021-8693
DOI: 10.1016/0021-8693(84)90046-2