scholarly journals Generating pairs of projective special linear groups that fail to lift

2020 ◽  
Vol 293 (7) ◽  
pp. 1251-1258
Author(s):  
Jan Boschheidgen ◽  
Benjamin Klopsch ◽  
Anitha Thillaisundaram
Keyword(s):  
Linear Groups ◽  
Special Linear ◽  
Projective Special Linear Groups ◽  
Special Linear Groups

RECOGNIZING BY ORDER AND DEGREE PATTERN OF SOME PROJECTIVE SPECIAL LINEAR GROUPS

2012 ◽  
Vol 22 (06) ◽  
pp. 1250051 ◽  
Author(s):  
B. AKBARI ◽  
A. R. MOGHADDAMFAR
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Linear Groups ◽  
Special Linear ◽  
Projective Special Linear Groups ◽  
Special Linear Groups ◽  
Isomorphism Classes ◽  
Degree Pattern ◽  
A Finite Group

Let M be a finite group and D (M) be the degree pattern of M. Denote by h OD (M) the number of isomorphism classes of finite groups G with the same order and degree pattern as M. A finite group M is called k-fold OD-characterizable if h OD (M) = k. Usually, a 1-fold OD-characterizable group is simply called OD-characterizable. The purpose of this article is twofold. First, it provides some information on the structure of a group from its degree pattern. Second, it proves that the projective special linear groups L4(4), L4(8), L4(9), L4(11), L4(13), L4(16), L4(17) are OD-characterizable.

scholarly journals PROJECTIVE SPECIAL LINEAR GROUPS PSL4(q) ARE DETERMINED BY THE SET OF THEIR CHARACTER DEGREES

2012 ◽  
Vol 11 (06) ◽  
pp. 1250108 ◽  
Author(s):  
HUNG NGOC NGUYEN ◽  
HUNG P. TONG-VIET ◽  
THOMAS P. WAKEFIELD
Keyword(s):  
Finite Group ◽  
Character Degrees ◽  
Linear Groups ◽  
Complex Character ◽  
Special Linear ◽  
Projective Special Linear Groups ◽  
Special Linear Groups ◽  
The Family ◽  
Group A ◽  
A Finite Group

Let G be a finite group and let cd (G) be the set of all irreducible complex character degrees of G. It was conjectured by Huppert in Illinois J. Math.44 (2000) that, for every non-abelian finite simple group H, if cd (G) = cd (H) then G ≅ H × A for some abelian group A. In this paper, we confirm the conjecture for the family of projective special linear groups PSL 4(q) with q ≥ 13.

scholarly journals Conjugacy classes in projective and special linear groups

1980 ◽  
Vol 22 (3) ◽  
pp. 339-364 ◽  
Author(s):  
G.E. Wall
Keyword(s):  
Finite Field ◽  
Conjugacy Classes ◽  
Linear Groups ◽  
Commutative Field ◽  
Special Linear ◽  
Projective Special Linear Groups ◽  
Special Linear Groups ◽  
Finite Dimensional

The conjugacy classes in the finite-dimensional projective full linear, special linear and projective special linear groups over an arbitrary commutative field are determined. The results over a finite field are applied to certain enumerative problems.

OD-Characterization of the Projective Special Linear Groups L2(q)

2012 ◽  
Vol 19 (03) ◽  
pp. 509-524 ◽  
Author(s):  
Liangcai Zhang ◽  
Wujie Shi
Keyword(s):  
Prime Graph ◽  
Simple Groups ◽  
Linear Groups ◽  
Finite Simple Groups ◽  
Projective Special Linear Group ◽  
Special Linear ◽  
Projective Special Linear Groups ◽  
Special Linear Groups

Let L2(q) be the projective special linear group, where q is a prime power. In the present paper, we prove that L2(q) is OD-characterizable by using the classification of finite simple groups. A new method is introduced in order to deal with the subtle changes of the prime graph of a group in the discussion of its OD-characterization. This not only generalizes a result of Moghaddamfar, Zokayi and Darafsheh, but also gives a positive answer to a conjecture put forward by Shi.

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