Generators of Maximal Subgroups of Harada-Norton and some Linear Groups

Open Chemistry

Haq Absar Ul¹  Yasin Faisal²  Farooq Adeel³  Liu Jia-Bao⁴ 

[1] Department of Basic Science and Humanities, University of Engineering and Technology, Lahore (Narowal Campus), LahorePakistan;Department of Mathematics and Statistics, The University of Lahore, Lahore54000, Pakistan;Department of Mathematics, COMSATS University Islamabad, Lahore Campus, LahorePakistan;School of Mathematics and Physics, Anhui Jianzhu University, Hefei230601, China;

关键词: harada-norton group;    maximal subgroup;    generators;    finite group;    normalizer;   

DOI  :  10.1515/chem-2019-0143

来源: DOAJ

【 摘 要 】

Group theory, the ultimate theory for symmetry, is a powerful tool that has a direct impact on research in robotics, computer vision, computer graphics and medical image analysis. Symmetry is very important in chemistry research and group theory is the tool that is used to determine symmetry. Usually, it is not only the symmetry of molecule but also the symmetries of some local atoms, molecular orbitals, rotations and vibrations of bonds, etc. that are important. Harada-Norton group is an example of a sporadic simple group. There are 14 maximal subgroups of Harada-Norton group. Generators (also known as words) of 11 maximal subgroups are already known. The aim of this note is to give generators of the remaining 3 maximal subgroups, which is an open problem mentioned on A World-wide-web Atlas of Group Representations (http://brauer.maths.qmul.ac.uk/Atlas) [1]. In this report we compute the generators of A6 × A6.D8, 23+2+6.(3 × L3(2)) and 34 : 2.(A4 × A4).4. Moreover we also compute the generators for the Maximal subgroups of some linear groups.

【 授权许可】

Unknown