Finite simple group type not classified as Lie, cyclic or alternating
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In the mathematical classification of finite simple groups, there are 26 or 27 groups which do not fit into any infinite family. These are called the sporadic simple groups, or the sporadic finite groups, or just the sporadic groups.
A simple group is a group G that does not have any normal subgroups except for the trivial group and G itself. The mentioned classification theorem states that the list of finite simple groups consists of 18 countably infinite families[a] plus 26 exceptions that do not follow such a systematic pattern. These 26 exceptions are the sporadic groups. The Tits group is sometimes regarded as a sporadic group because it is not strictly a group of Lie type,[1] in which case there would be 27 sporadic groups.
The monster group, or friendly giant, is the largest of the sporadic groups, and all but six of the other sporadic groups are subquotients of it.[2]
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simple groups, there are 26 or 27 groups which do not fit into any infinite family. These are called the sporadic simple groups, or the sporadic finite...
In the area of modern algebra known as group theory, the Suzuki group Suz or Sz is a sporadic simple group of order 213 · 37 · 52 · 7 · 11 · 13 = 448345497600...
The qualification sporadic, indicating that occurrences of some phenomenon are rare and not systematic, can be used for: Sporadicgroup, any of a small...
group. The five Mathieu groups constitute the first generation in the happy family of sporadicgroups. These are also the first five sporadicgroups to...
pair. The Tits group is member of the infinite family 2F4(22n+1)′ of commutator groups of the Ree groups, and thus by definition not sporadic. But because...
In group theory, a topic in abstract algebra, the Mathieu groups are the five sporadic simple groups M11, M12, M22, M23 and M24 introduced by Mathieu (1861...
known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group, having...
While only two sporadicgroups have eight prime factors in their order (Lyons group L y {\displaystyle \mathrm {Ly} } and Fischer group F i 23 {\displaystyle...
classification of finite simple groups, twenty of twenty-six sporadicgroups in the happy family are part of three families of groups which divide the order of...
the first modern sporadicgroup. They have involution centralizers of the form Z/2Z × PSL(2, q) for q = 3n, and by investigating groups with an involution...
group theory, the Mathieu group M11 is a sporadic simple group of order 24 · 32 · 5 · 11 = 11 · 10 · 9 · 8 = 7920. M11 is one of the 26 sporadic groups...
groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadicgroups....
modern algebra known as group theory, the baby monster group B (or, more simply, the baby monster) is a sporadic simple group of order 4,154,781,481...
infinite class called the groups of Lie type, or else it is one of twenty-six or twenty-seven exceptions, called sporadic. The proof consists of tens...
algebra known as group theory, the Conway groups are the three sporadic simple groups Co1, Co2 and Co3 along with the related finite group Co0 introduced...
In the area of modern algebra known as group theory, the McLaughlin group McL is a sporadic simple group of order 27 ⋅ 36 ⋅ 53 ⋅ 7 ⋅ 11 = 898,128,000...
In the area of modern algebra known as group theory, the Rudvalis group Ru is a sporadic simple group of order 214 · 33 · 53 · 7 · 13 · 29 = 145926144000...
families of groups as well as 26 additional groups which do not fit into any family. The latter groups are called the "sporadic" groups, and each one...
other than the cyclic groups, the alternating groups, the Tits group, and the 26 sporadic simple groups. For any finite group G, the order (number of...
area of modern algebra known as group theory, the Lyons group Ly or Lyons-Sims group LyS is a sporadic simple group of order 28 · 37 · 56 · 7 · 11 ·...
In mathematics, the term Thompson group or Thompson's group can refer to either The finite Thompson sporadicgroup Th studied by John G. Thompson The finite...
area of modern algebra known as group theory, the Janko group J2 or the Hall-Janko group HJ is a sporadic simple group of order 27 · 33 · 52 · 7 = 604800...
known as group theory, the Janko groups are the four sporadic simple groups J1, J2, J3 and J4 introduced by Zvonimir Janko. Unlike the Mathieu groups, Conway...
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