scholarly journals A Characterization of Alternating Group A28 by Conjugate Class Sizes

2015 ◽  
Vol 15 (3) ◽  
pp. 588-592
Author(s):  
Shitian Liu
Keyword(s):  
Alternating Group ◽  
Conjugate Class

scholarly journals OD-characterization of alternating groups Ap+d

2017 ◽  
Vol 15 (1) ◽  
pp. 1090-1098
Author(s):  
Yong Yang ◽  
Shitian Liu ◽  
Zhanghua Zhang
Keyword(s):  
The Other ◽  
Alternating Group ◽  
Alternating Groups ◽  
Other Hand

Abstract Let An be an alternating group of degree n. Some authors have proved that A10, A147 and A189 cannot be OD-characterizable. On the other hand, others have shown that A16, A23+4, and A23+5 are OD-characterizable. We will prove that the alternating groups Ap+d except A10, are OD-characterizable, where p is a prime and d is a prime or equals to 4. This result generalizes other results.

scholarly journals Characterization of the alternating group by its non-commuting graph

2012 ◽  
Vol 357 ◽  
pp. 203-207 ◽  
Author(s):  
Alireza Abdollahi ◽  
Hamid Shahverdi
Keyword(s):  
Alternating Group ◽  
Commuting Graph

A CHARACTERIZATION OF ALTERNATING GROUPS BY ORDERS OF SOLVABLE SUBGROUPS

2004 ◽  
Vol 03 (04) ◽  
pp. 445-452 ◽  
Author(s):  
JIANXING BI ◽  
XIANHUA LI
Keyword(s):  
Finite Group ◽  
Alternating Group ◽  
Alternating Groups ◽  
Group A ◽  
A Finite Group

In this paper, we prove that a finite group G is isomorphic to the alternating group An with n≥5 if and only if they have the same set of the orders of solvable subgroups.

Integral Group Rings of Some p-Groups

1982 ◽  
Vol 34 (1) ◽  
pp. 233-246 ◽  
Author(s):  
Jürgen Ritter ◽  
Sudarshan Sehgal
Keyword(s):  
Dihedral Group ◽  
Alternating Group ◽  
Group Rings ◽  
Integral Group ◽  
Product Decomposition ◽  
Integral Group Rings ◽  
Group Of Units ◽  
Wedderburn Decomposition ◽  
Fibre Product

1. Introduction. The group of units, , of the integral group ring of a finite non-abelian group G is difficult to determine. For the symmetric group of order 6 and the dihedral group of order 8 this was done by Hughes-Pearson [3] and Polcino Milies [5] respectively. Allen and Hobby [1] have computed , where A4 is the alternating group on 4 letters. Recently, Passman-Smith [6] gave a nice characterization of where D2p is the dihedral group of order 2p and p is an odd prime. In an earlier paper [2] Galovich-Reiner-Ullom computed when G is a metacyclic group of order pq with p a prime and q a divisor of (p – 1). In this note, using the fibre product decomposition as in [2], we give a description of the units of the integral group rings of the two noncommutative groups of order p3, p an odd prime. In fact, for these groups we describe the components of ZG in the Wedderburn decomposition of QG.

Finite groups with exactly one composite character degree

2016 ◽  
Vol 15 (07) ◽  
pp. 1650132 ◽  
Author(s):  
Yan-Jun Liu ◽  
Yang Liu
Keyword(s):  
Finite Groups ◽  
Character Degree ◽  
Alternating Group ◽  
Direct Factor ◽  
Irreducible Characters

Motivated by Isaacs and Passman’s characterization of finite groups all of whose nonlinear complex irreducible characters have prime degrees, we investigate finite groups [Formula: see text] with exactly one character degree that is not a prime. We show that either [Formula: see text] is solvable with [Formula: see text] or [Formula: see text] for distinct primes [Formula: see text], or up to an abelian direct factor, [Formula: see text] is isomorphic to the alternating group [Formula: see text].

scholarly journals A characterization of the Petersen-type geometry of the McLaughlin group

2000 ◽  
Vol 128 (1) ◽  
pp. 21-44 ◽  
Author(s):  
B. BAUMEISTER ◽  
A. A. IVANOV ◽  
D. V. PASECHNIK
Keyword(s):  
Automorphism Group ◽  
Universal Cover ◽  
Classification Problem ◽  
Alternating Group ◽  
Sporadic Simple Group ◽  
Mathieu Group ◽  
Transitive Automorphism Group ◽  
The Right ◽  
Simply Connected

The McLaughlin sporadic simple group McL is the flag-transitive automorphism group of a Petersen-type geometry [Gscr ] = [Gscr ](McL) with the diagramdiagram herewhere the edge in the middle indicates the geometry of vertices and edges of the Petersen graph. The elements corresponding to the nodes from the left to the right on the diagram P33 are called points, lines, triangles and planes, respectively. The residue in [Gscr ] of a point is the P3-geometry [Gscr ](Mat22) of the Mathieu group of degree 22 and the residue of a plane is the P3-geometry [Gscr ](Alt7) of the alternating group of degree 7. The geometries [Gscr ](Mat22) and [Gscr ](Alt7) possess 3-fold covers [Gscr ](3Mat22) and [Gscr ](3Alt7) which are known to be universal. In this paper we show that [Gscr ] is simply connected and construct a geometry [Gscr ]˜ which possesses a 2-covering onto [Gscr ]. The automorphism group of [Gscr ]˜ is of the form 323McL; the residues of a point and a plane are isomorphic to [Gscr ](3Mat22) and [Gscr ](3Alt7), respectively. Moreover, we reduce the classification problem of all flag-transitive Pmn-geometries with n, m [ges ] 3 to the calculation of the universal cover of [Gscr ]˜.

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