On a characteristic property of finite sets
نویسندگان
چکیده
منابع مشابه
ON 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 کاملFinite Special Moufang Sets of Odd Characteristic
In this paper we classify finite special Moufang sets M(U, τ ) of odd characteristic. The characteristic 2 case was handled in another paper by De Medts and the author. We prove, using elementary means that U is elementary abelian. Then we show that M(U, τ ) is the unique Moufang set whose little projective group is PSL2(|U |). The emphasis of this paper is on obtaining elementary proofs. Secti...
متن کاملOn semi-$Pi$-property of subgroups of finite group
Let $G$ be a group and $H$ a subgroup of $G$. $H$ is said to have semi-$Pi$-property in $G$ if there is a subgroup $T$ of $G$ such that $G=HT$ and $Hcap T$ has $Pi$-property in $T$. In this paper, investigating on semi-$Pi$-property of subgroups, we shall obtain some new description of finite groups.
متن کاملOn a Covering Property of Convex Sets
Let [Kx, K2, ■ ■ ■ } be a class of compact convex subsets of euclidean M-space with the property that the set of their diameters is bounded. It is shown that the sets A, can be rearranged by the application of rigid motions so as to cover the total space if and only if the sum of the volumes of all the sets A, is infinite. Also, some statements regarding the densities of such coverings are prov...
متن کاملExtensions of ordered sets having the finite cutset property
Let P be an ordered set. P is said to have the finite cutset property if for every x in P there is a finite set F of elements which are noncomparable to x such that every maximal chain in P meets {x} t.J F. It is well known that this property is equivalent to the space of maximal chains of P being compact. We consider the following question: Which ordered sets P can be embedded in an ordered se...
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: Pacific Journal of Mathematics
سال: 1952
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1952.2.323