scholarly journals A new characterization of projective special linear groups L3(q)

2021 ◽  
Vol 31 (2) ◽  
pp. 212-218
Author(s):  
B. Ebrahimzadeh ◽  
Keyword(s):  
Prime Number ◽  
Linear Groups ◽  
Special Linear ◽  
Projective Special Linear Groups ◽  
Special Linear Groups

In this paper, we prove that projective special linear groups L3(q), where 0<q=5k±2 (k∈Z) and q2+q+1 is a~prime number can be uniquely determined by their order and the number of elements with same order.

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.

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.

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