Introduction to Sporadic Groups
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 increasi...
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| Format: | Article |
| Language: | English |
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National Academy of Science of Ukraine
2011-01-01
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.3842/SIGMA.2011.009 |
| _version_ | 1819096409686671360 |
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| author | Luis J. Boya |
| author_facet | Luis J. Boya |
| author_sort | Luis J. Boya |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-21T23:58:44Z |
| format | Article |
| id | doaj.art-3e9c97dd9bf24c8b929a3c1388818668 |
| institution | Directory Open Access Journal |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2024-12-21T23:58:44Z |
| publishDate | 2011-01-01 |
| publisher | National Academy of Science of Ukraine |
| record_format | Article |
| series | Symmetry, Integrability and Geometry: Methods and Applications |
| spelling | doaj.art-3e9c97dd9bf24c8b929a3c13888186682022-12-21T18:45:45ZengNational Academy of Science of UkraineSymmetry, Integrability and Geometry: Methods and Applications1815-06592011-01-017009Introduction to Sporadic GroupsLuis J. BoyaThis 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.http://dx.doi.org/10.3842/SIGMA.2011.009group theoryfinite groups |
| spellingShingle | Luis J. Boya Introduction to Sporadic Groups Symmetry, Integrability and Geometry: Methods and Applications group theory finite groups |
| title | Introduction to Sporadic Groups |
| title_full | Introduction to Sporadic Groups |
| title_fullStr | Introduction to Sporadic Groups |
| title_full_unstemmed | Introduction to Sporadic Groups |
| title_short | Introduction to Sporadic Groups |
| title_sort | introduction to sporadic groups |
| topic | group theory finite groups |
| url | http://dx.doi.org/10.3842/SIGMA.2011.009 |
| work_keys_str_mv | AT luisjboya introductiontosporadicgroups |