scholarly journals The Largest Prime Dividing the Maximal Order of an Element of S n

1995 ◽  
Vol 64 (209) ◽  
pp. 407 ◽  
Author(s):  
Jon Grantham
1989 ◽  
Vol 53 (188) ◽  
pp. 665-665 ◽  
Author(s):  
Jean-Pierre Massias ◽  
Jean-Louis Nicolas ◽  
Guy Robin

2021 ◽  
pp. 33-38
Author(s):  
Faraj. A. Abdunabi

This study was aimed to consider the NG-group that consisting of transformations on a nonempty set A has no bijection as its element. In addition, it tried to find the maximal order of these groups. It found the order of NG-group not greater than n. Our results proved by showing that any kind of NG-group in the theorem be isomorphic to a permutation group on a quotient set of A with respect to an equivalence relation on A. Keywords: NG-group; Permutation group; Equivalence relation; -subgroup


1988 ◽  
Vol 30 (2) ◽  
pp. 231-236
Author(s):  
Shigeaki Tsuyumine

Let K be a totally real algebraic number field of degree n > 1, and let OK be the maximal order. We denote by гk, the Hilbert modular group SL2(OK) associated with K. On the extent of the weight of an automorphy factor for гK, some restrictions are imposed, not as in the elliptic modular case. Maass [5] showed that the weight is integral for K = ℚ(√5). It was shown by Christian [1] that for any Hilbert modular group it is a rational number with the bounded denominator depending on the group.


10.37236/5441 ◽  
2017 ◽  
Vol 24 (1) ◽  
Author(s):  
Michael Coons ◽  
Lukas Spiegelhofer

Using methods developed by Coons and Tyler, we give a new proof of a recent result of Defant, by determining the maximal order of the number of hyper-($b$-ary)-expansions of a nonnegative integer $n$ for general integral bases $b\geqslant 2$.


2019 ◽  
Vol 39 (1) ◽  
pp. 115-130
Author(s):  
Domingo González ◽  
◽  
Gamaliel Blé
Keyword(s):  

1992 ◽  
Vol 35 (2) ◽  
pp. 255-269 ◽  
Author(s):  
A. W. Chatters ◽  
M. P. Gilchrist ◽  
D. Wilson

Let R be a ring. An element p of R is a prime element if pR = Rp is a prime ideal of R. A prime ring R is said to be a Unique Factorisation Ring if every non-zero prime ideal contains a prime element. This paper develops the basic theory of U.F.R.s. We show that every polynomial extension in central indeterminates of a U.F.R. is a U.F.R. We consider in more detail the case when a U.F.R. is either Noetherian or satisfies a polynomial identity. In particular we show that such a ring R is a maximal order, that every height-1 prime ideal of R has a classical localisation in which every two-sided ideal is principal, and that R is the intersection of a left and right Noetherian ring and a simple ring.


2021 ◽  
Vol 567 ◽  
pp. 269-283
Author(s):  
P. Longobardi ◽  
M. Maj ◽  
P. Shumyatsky ◽  
G. Traustason
Keyword(s):  

2020 ◽  
Vol 46 (5) ◽  
Author(s):  
Michael S. Floater ◽  
Kaibo Hu

Abstract We consider spline functions over simplicial meshes in $\mathbb {R}^{n}$ ℝ n . We assume that the spline pieces join together with some finite order of smoothness but the pieces themselves are infinitely smooth. Such splines can have extra orders of smoothness at a vertex, a property known as supersmoothness, which plays a role in the construction of multivariate splines and in the finite element method. In this paper, we characterize supersmoothness in terms of the degeneracy of spaces of polynomial splines over the cell of simplices sharing the vertex, and use it to determine the maximal order of supersmoothness of various cell configurations.


1979 ◽  
Vol 26 (3) ◽  
pp. 527-537 ◽  
Author(s):  
Arthur G. Werschulz

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