O'Nan group

Group theory
Group theory
Basic notions Subgroup Normal subgroup Quotient group Group homomorphism (semi-)direct product
Finite groups (classification) Cyclic group Zn Symmetric group, Sn Dihedral group, Dn Alternating group An Mathieu groups M11, M12, M22, M23, M24 Conway groups Co1, Co2, Co3 Janko groups J1, J2, J3, J4 Fischer groups F22, F23, F24 Baby Monster group B Monster group M
Discrete groups and lattices The integers, Z Lattice (group) Modular groups, PSL(2,Z) and SL(2,Z)
Topological groups and Lie groups Solenoid (mathematics) Circle group General linear group GL(n) Special linear group SL(n) Orthogonal group O(n) Special orthogonal group SO(n) Unitary group U(n) Special unitary group SU(n) Symplectic group Sp(n) G2 F4 E6 E7 E8 Lorentz group Poincaré group Conformal group Diffeomorphism group Loop group Infinite-dimensional Lie groups O(∞) SU(∞) Sp(∞)
v · mathematical field of group theory, the O'Nan group O'N is a sporadic simple group of order    29 · 34 · 5 · 73 · 11 · 19 · 31 = 460815505920 It was found by Michael O'Nan (1976) in a study of groups with a Sylow 2-subgroup of "Alperin type", meaning isomorphic to a Sylow 2-Subgroup of a group of type (Z/2nZ ×Z/2nZ ×Z/2nZ).PSL3(F2). The Schur multiplier has order 3, and its outer automorphism group has order 2. Its triple cover has two 45-dimensional representations over the field with 7 elements, exchanged by an outer automorphism (Ryba 1988). The subgroup fixed by an outer automorphism of order 2 is the Janko group J1, a maximal subgroup. O'N is one of the 6 sporadic simple groups called the pariahs, because they are not found within the Monster group. References O'Nan, Michael E. (1976), "Some evidence for the existence of a new simple group", Proceedings of the London Mathematical Society. Third Series 32 (3): 421–479, doi:10.1112/plms/s3-32.3.421, ISSN 0024-6115, MR0401905  R. L. Griess, Jr, The Friendly Giant, Inventiones Mathematicae 69 (1982), 1-102. p. 94: proof that O'N is a pariah. A. J. E. Ryba, A new construction of the O'Nan simple group. J. Algebra 112 (1988), no. 1, 173-197.MR0921973 Atlas of Finite Group Representations: O'Nan group Wikimedia Foundation. 2010. Игры ⚽ Поможем написать реферат Shimazu Hisamitsu Return receipt Look at other dictionaries: Nan Hayworth — Member of the U.S. House of Representatives from New York s 19th district Incumbent Assumed office Janu …   Wikipedia Nan Quan Mama — Chinese name 南拳媽媽 (Traditional) Chinese name 南拳妈妈 (Simplified) Pinyin Nán Quán Māmā (Mandarin) Origin …   Wikipedia Nan Fung Group — (Chinese: 南豐集團) is a privately held group of companies carrying on the business of property development as its core business in Greater China including shipping, textiles and financial services. It is also one of the leading property developers… …   Wikipedia Nan Hua High School — 南华中学 忠，孝，仁，爱，礼，仪，廉，耻 Location 41 Clementi Ave 1, Singapore 129956 Nearest MRT Stations: Clementi, Dover …   Wikipedia Nan Cross — (born January 3, 1928 July 14, 2007, Yeoville, Johannesburg, South Africa) was a South African anti apartheid and anti conscription activist. Contents 1 Early life 2 Social activism 2.1 Conscientious objectors movement …   Wikipedia Nan Phelps — (Approx. 1940) Birth name Nannie Dorothea Hinkle Born August 25, 1904(1904 08 25 …   Wikipedia Nan Huai-Chin — in 1945, after descending Mount Emei from his hermitage. Nan Huai Chin (born 1918) (simplified Chinese: 南怀瑾; traditional Chinese: 南懷瑾; pinyin: Nán Huáijǐn) is a spiritual teacher of contemporary Ch …   Wikipedia Nan Fung Centre — (Chinese: 南豐中心) is a commercial and shopping centre in Castle Peak Road, Tsuen Wan, New Territories, Hong Kong, located nearby the MTR Tsuen Wan Station and a bus ter …   Wikipedia Nan Hua Primary School — 忠孝仁爱 礼义廉耻 (Loyalty, Filial Piety, Humanity, Love, Courtesy, Righteousness, Integrity, Sense of Shame) Location 30 Jalan Lempeng …   Wikipedia Nan Kempner — (July 24, 1930 July 3, 2005) was a New York City socialite, famous for dominating society events, shopping, charity work and fashion. She was born as Nan Field Schlesinger in San Francisco, an only child from a wealthy family. Her father, Albert… …   Wikipedia 18+ © Academic, 2000-2024 Contact us: Technical Support, Advertising Dictionaries export, created on PHP, Joomla, Drupal, WordPress, MODx. Mark and share Search through all dictionaries Translate… Search Internet Share the article and excerpts Direct link … Do a right-click on the link above and select “Copy Link”