Regular Subgroups of a Transitive Substitution Group.
نویسنده
چکیده
منابع مشابه
ON FINITE GROUPS IN WHICH SS-SEMIPERMUTABILITY IS A TRANSITIVE RELATION
Let H be a subgroup of a finite group G. We say that H is SS-semipermutable in Gif H has a supplement K in G such that H permutes with every Sylow subgroup X of Kwith (jXj; jHj) = 1. In this paper, the Structure of SS-semipermutable subgroups, and finitegroups in which SS-semipermutability is a transitive relation are described. It is shown thata finite solvable group G is a PST-group if and on...
متن کاملOn the socles of characteristic subgroups of Abelian p-groups
Fully invariant subgroups of an Abelian p-group have been the object of a good deal of study, while characteristic subgroups have received somewhat less attention. Recently the socles of fully invariant subgroups have been studied and this led to the notion of a socle-regular group. The present work replaces the fully invariant subgroups with characteristic ones and leads in a natural way to th...
متن کاملGroups Generated by Two Operators of the Same Prime Order Such That the Conjugates of One under the Powers of the Other Are Commutative. by Peopessok
IN a previous article,* devoted to a study of conjugate operators, attention was called to the fact that a complete set of conjugate operators which are not all relatively commutative is transformed under the group according to a substitution group which is at most triply transitive. It is easy to prove that this substitution group is at most doubly transitive, and, as the p conjugates of order...
متن کاملMultiply Transitive Substitution Groups*
A substitution group G of degree n is said to be r-fold transitive if each of the n(n — 1) • • • (n—r + 1) permutations of its n letters taken r at a time is represented by at least one substitution of G. It is not sufficient to say that each of its possible sets of r letters is transformed into every one of these sets by the substitutions of G. For instance, in each of the semi-metacyclic grou...
متن کاملObservations upon Complement Fixation in Infections with Endamoeba Histolytica.
special interest. Let G1 represent one such subgroup and suppose that the degree of G is n, while the number of its transitive constituents is k. It will be convenient to think of G1 as having as many conjugates under G as the degree of the transitive constituent of G which involves the letter omitted by all the substitutions of G1. Two conjugates of G need therefore not be distinct. If a subst...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Proceedings of the National Academy of Sciences of the United States of America
دوره 22 6 شماره
صفحات -
تاریخ انتشار 1936