Sylow (aNowegian mathematician) in his theorem gave a condition for such divisor mif G must have a subgroup of order m. The group treated in this paper is thepermutation group also called the symmetric group. Wreath product is usedin constructing these subgroups (the Sylow p - subgroups) of...
We call a group G an MS-group if the maximal subgroups of all the Sylow subgroups of G are S-semipermutable. MS-groups are known to be supersolvable and we show that the nilpotent residual of an MS-group is a nilpotent Hall subgroup of G. Moreover, we show that if G is an MS-...
Let q q be a power of a prime p p and let U(q) U(q) be a Sylow p p -subgroup of a finite Chevalley group G(q) G(q) defined over the field with q q elements. We first give a parametrization of the set ext{Irr}(U(q)) ext{Irr}(U(q)) o... T Le,K Magaard,A Pao...
D. L. Shaw, "The Sylow 2-subgroups of finite, soluble groups with a single class of involutions," J. Algebra, 16 , No. 1, 14–26 (1970).Shaw, D. L. (1970) The Sylow 2-subgroups of finite, soluble groups with a single class of involutions. J. Algebra 16: pp. 14-26...
The Sylow Theorem states that if a group is cyclic then all Sylow subgroups are cyclic. If the group is not cyclic then that theorem does not hold true. This theorem proves to be useful in many real-world scenarios, such as when trying to understand which subgroups have certain orders....
Our theorem, combined with the main results of [5] and [6], shows that there is no simple group whose Sylow 2-subgroups satisfy the conditions of Thompson's result. Since many of the arguments of this paper are quite similar to corresponding ones in [6], we have omitted the proofs of...
摘要: A subgroup H of G is said to be M-normal in G if there exists a normal subgroup B of G such that G=HB and H1BG for every maximal subgroup H1 of H.Some new results about p-nilpotency and formation are obtained by using M-normal of the Sylow subgroup in group G.关键词:...
We determine the character tables of Sylow $p$-subgroups ${^3}D_4^{syl}(q^3)$ of the Steinberg triality groups ${^3}D_4(q^3)$.doi:10.1080/00927872.2018.1461881Yujiao SunCommunications in AlgebraY. Sun. Character tables of Sylow p-subgroups 3D4syl(q3) of the Steinberg triality ...
The Sylow subgroups of X are described in [17, Satz 8.15, p. 505]. Suppose that X is soluble. Let r and s be primes dividing |X| and a and b be elements of order r and s respectively. If X has odd order then a and b commute by [17, Satz 8.16(b), p. 506]. If X has...
Define Alternating groups. Alternating groups synonyms, Alternating groups pronunciation, Alternating groups translation, English dictionary definition of Alternating groups. n. A group consisting of all possible even permutations of a given number of it