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...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2011 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2011
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146797 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Introduction to Sporadic Groups / L.J. Boya // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 34 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862655542812475392 |
|---|---|
| author | Boya, L.J. |
| author_facet | Boya, L.J. |
| citation_txt | Introduction to Sporadic Groups / L.J. Boya // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 34 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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 | 2025-12-02T03:29:07Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146797 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T03:29:07Z |
| publishDate | 2011 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Boya, L.J. 2019-02-11T15:23:01Z 2019-02-11T15:23:01Z 2011 Introduction to Sporadic Groups / L.J. Boya // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 34 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 20D08; 20F99 DOI:10.3842/SIGMA.2011.009 https://nasplib.isofts.kiev.ua/handle/123456789/146797 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. This paper is a contribution to the Proceedings of the Workshop “Supersymmetric Quantum Mechanics and Spectral Design” (July 18–30, 2010, Benasque, Spain). The full collection is available at http://www.emis.de/journals/SIGMA/SUSYQM2010.html.
 Work supported by grant A/9335/07 of the PCI-AECI and grant 2007-E24/2 of DGIID-DGA. The author thanks Professors A. Andrianov (Barcelona) and L.M. Nieto (Valladolid) for the opportunity to present the material as a Seminar in the Conference on Supersymmetric Quantum Mechanics. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Introduction to Sporadic Groups Article published earlier |
| spellingShingle | Introduction to Sporadic Groups Boya, L.J. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146797 |
| work_keys_str_mv | AT boyalj introductiontosporadicgroups |