Contemporary MathematicsEnumerating subgroups of the symmetric groupDerek F. HoltAbstract. We announce our successful computation of a list of representa-tives of the conjugacy classes of subgroups of S n for n ≤ 18, including the7274651 classes of subgroups of S 18 .1. IntroductionEarly ...
This thesis addresses the question of which subgroups G of the finite symmetric group Sn contain an n-cycle.; The solution to the case n = p a prime is based on a theorem of Burnside. When n is not prime, we apply a theorem based on results of Burnside and Schur to see that the ...
Sylow subgroups of symmetric and alternating groups and the vertex of $S^{(kp-p,1^p)}$ in characteristic $p$ We show that the Sylow $p$-subgroups of a symmetric group, respectively an alternating group, are characterized as the $p$-subgroups containing all element... E Giannelli,KJ Lim...
GROUP-ALGEBRA EXTENSIONSLet n and k be positive integers. We consider the (ordinary) depth of several Young subgroups of the symmetric group S-n. For k = 2k, we show that the depth of S-{k+1,S-...,S-n} x S-{1,S-...,S-k} similar or equal to Sn-k x S-k in S-n is...
For a finite group G, let (G) denote the sum of element orders of G. The aim of this article is to show that (H) < (An) for every proper subgroup H of the symmetric group of degree n, which is different from the alternating group An.关键词: Element orders Maximal subgroups Symme...
Let Γ = GSp (2l, R) be the general symplectic group of rank l over a commutative ring R such that 2 ∈ R*; and let ν be a symmetric equivalence relation on the index set {1,…, l, l,…, 1} all of whose classes contain at least 3 elements. In the present paper, we ...
In 1976, the structure of locally finite groups S() (respectively A() ) which are obtained as a direct limit of finite symmetric (finite alternating) groups are investigated in [7]. The countable locally finite groups A() gives an important class in the theory of infinite simple locally ...
group G such that the symmetric space D of maximal compact subgroups of the real Lie group G(R) is a hermitian symmetric space of the non-compact type. There are two major classes of subgroups of G of importance to the geometry of D and to arithmetic quotients X Γ = Γ\D of D: ...
It is thesymmetric group on a set of three elements, viz., the group of all permutations of a three-element set. In particular, it is a symmetric group of prime degree and symmetric group of prime power degree. Is Z1 cyclic?
Although Brauer groups are well studied from a theoretical point of view, no one has yet addressed the question of making this theory explicit. We prop... K Nguyen 被引量: 27发表: 2001年 Normal subgroups of nonstandard symmetric and alternating groups Let ${mathfrak{M}}$ be a non...