In this article, we give a short proof for the existence and uniqueness of the Higman-Sims sporadic simple group HS by means of the first author's algorithm [17] and uniqueness criterion [18], respectively. We realize HS as a subgroup of GL22(11), and determine its automorphism group Aut(HS). We also give a presentation for Aut(HS) in terms of generators and relations. Furthermore, the character table of HS is determined and representatives of its conjugacy classes are given as short words in its generating matrices inside GL22(11). © 2005 AMSS CAS & SUZHOU UNIV.
Michler, G., Previtali, A. (2005). Another existence and uniqueness proof for the higman-sims simple group. ALGEBRA COLLOQUIUM, 12(3), 369-398.
Another existence and uniqueness proof for the higman-sims simple group
PREVITALI, ANDREA
2005
Abstract
In this article, we give a short proof for the existence and uniqueness of the Higman-Sims sporadic simple group HS by means of the first author's algorithm [17] and uniqueness criterion [18], respectively. We realize HS as a subgroup of GL22(11), and determine its automorphism group Aut(HS). We also give a presentation for Aut(HS) in terms of generators and relations. Furthermore, the character table of HS is determined and representatives of its conjugacy classes are given as short words in its generating matrices inside GL22(11). © 2005 AMSS CAS & SUZHOU UNIV.
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