2011/01/16 by Luis J. Boya · 6 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Classification of finite simple groups #Combinatorics #Finite Group Theory Research #Group (periodic table) #Group of Lie type #Group theory #Mathematics #Pariah group #Physics #Pure mathematics #Simple (philosophy) #Simple group #Sporadic group #hep-th #math-ph #math.GR #math.MP
paper · pdf · doi:10.3842/sigma.2011.009
published in Symmetry Integrability and Geometry Methods and Applications (National Academy of Sciences of Ukraine)
arxiv created 2011/01/16 · openalex publication_date 2011/01/16 · arxiv updated 2015/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This is an introduction to finite simple groups, in particular sporadic groups, intended for physicists. After a short review of group theory, we enumerate the 1 + 1 + 16 = 18 families of finite simple groups, as an introduction to the sporadic groups. These are described next, in three levels of increasing complexity, plus the six isolated "pariah" groups. The (old) five Mathieu groups make up the first, smallest order level. The seven groups related to the Leech lattice, including the three Conway groups, constitute the second level. The third and highest level contains the Monster group M, plus seven other related groups. Next a brief mention is made of the remaining six pariah groups, thus completing the 5 + 7 + 8 + 6 = 26 sporadic groups. The review ends up with a brief discussion of a few of physical applications of finite groups in physics, including a couple of recent examples which use sporadic groups.