Solving the Class Equation x<sup>d</sup> = β in an Alternating Group for Each β ∈ C<sup>α</sup> ∩ H<sub>n</sub><sup>c</sup> and n > 1

2012 ◽  
Vol 02 (02) ◽  
pp. 13-19 ◽  
Author(s):  
Shuker Mahmood ◽  
Andrew Rajah
Keyword(s):  
Alternating Group

Panconnectivity, fault-tolerant hamiltonicity and hamiltonian-connectivity in alternating group graphs

Networks ◽  
2004 ◽  
Vol 44 (4) ◽  
pp. 302-310 ◽  
Author(s):  
Jou-Ming Chang ◽  
Jinn-Shyong Yang ◽  
Yue-Li Wang ◽  
Yuwen Cheng
Keyword(s):  
Fault Tolerant ◽  
Alternating Group ◽  
Hamiltonian Connectivity

scholarly journals Rational Trinomials with the Alternating Group as Galois Group

2001 ◽  
Vol 90 (1) ◽  
pp. 113-129 ◽  
Author(s):  
Alain Hermez ◽  
Alain Salinier
Keyword(s):  
Galois Group ◽  
Alternating Group

A new modified group explicit iterative method for the numerical solution of time dependent viscous Burgers' equation

2014 ◽  
Vol 05 (02) ◽  
pp. 1350029 ◽  
Author(s):  
Jyoti Talwar ◽  
R. K. Mohanty
Keyword(s):  
Iterative Method ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Iterative Methods ◽  
Iteration Method ◽  
Burgers Equation ◽  
Time Dependent ◽  
Alternating Group ◽  
Explicit Method ◽  
Rectangular Coordinates

In this article, we discuss a new smart alternating group explicit method based on off-step discretization for the solution of time dependent viscous Burgers' equation in rectangular coordinates. The convergence analysis for the new iteration method is discussed in details. We compared the results of Burgers' equation obtained by using the proposed iterative method with the results obtained by other iterative methods to demonstrate computationally the efficiency of the proposed method.

Fault-tolerant cycle-embedding in alternating group graphs

2008 ◽  
Vol 197 (2) ◽  
pp. 760-767 ◽  
Author(s):  
Jou-Ming Chang ◽  
Jinn-Shyong Yang
Keyword(s):  
Fault Tolerant ◽  
Alternating Group

Subgroups of the Alternating Group: 10480

1998 ◽  
Vol 105 (3) ◽  
pp. 275
Author(s):  
Shmuel Rosset ◽  
A. N. 't Woord
Keyword(s):  
Alternating Group

On Unsolvable Groups of Degree p = 4q + 1, p and q Primes

1967 ◽  
Vol 19 ◽  
pp. 583-589 ◽  
Author(s):  
K. I. Appel ◽  
E. T. Parker
Keyword(s):  
Permutation Group ◽  
Alternating Group ◽  
Transitive Permutation Group ◽  
University Of Illinois ◽  
The University

This paper presents two results. They are:Theorem 1. Let G be a doubly transitive permutation group of degree nq + 1 where a is a prime and n < g. If G is neither alternating nor symmetric, then G has Sylow q-subgroup of order only q.Result 2. There is no unsolvable transitive permutation group of degree p = 29, 53, 149, 173, 269, 293, or 317 properly contained in the alternating group of degree p.Result 2 was demonstrated by a computation on the Illiac II computer at the University of Illinois.

scholarly journals Gamma Positivity of the Descent Based Eulerian Polynomial in Positive Elements of Classical Weyl Groups

10.37236/9037 ◽  
2020 ◽  
Vol 27 (3) ◽  
Author(s):  
Hiranya Kishore Dey ◽  
Sivaramakrishnan Sivasubramanian
Keyword(s):  
Coxeter Groups ◽  
Weyl Groups ◽  
Alternating Group ◽  
Type B ◽  
Eulerian Polynomial ◽  
Eulerian Polynomials ◽  
Type D ◽  
Positive Elements

The Eulerian polynomial $A_n(t)$ enumerating descents in $\mathfrak{S}_n$ is known to be gamma positive for all $n$. When enumeration is done over the type B and type D Coxeter groups, the type B and type D Eulerian polynomials are also known to be gamma positive for all $n$. We consider $A_n^+(t)$ and $A_n^-(t)$, the polynomials which enumerate descents in the alternating group $\mathcal{A}_n$ and in $\mathfrak{S}_n - \mathcal{A}_n$ respectively.  We show the following results about $A_n^+(t)$ and $A_n^-(t)$: both polynomials are gamma positive iff $n \equiv 0,1$ (mod 4). When $n \equiv 2,3$ (mod 4), both polynomials are not palindromic. When $n \equiv 2$ (mod 4), we show that {\sl two} gamma positive summands add up to give $A_n^+(t)$ and $A_n^-(t)$. When $n \equiv 3$ (mod 4), we show that {\sl three} gamma positive summands add up to give both $A_n^+(t)$ and $A_n^-(t)$.  We show similar gamma positivity results about the descent based type B and type D Eulerian polynomials when enumeration is done over the positive elements in the respective Coxeter groups. We also show that the polynomials considered in this work are unimodal.

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