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Each group is named by Small Groups library as G o i, where o is the order of the group, and i is the index used to label the group within that order. Common group names: Z n: the cyclic group of order n (the notation C n is also used; it is isomorphic to the additive group of Z/nZ) Dih n: the dihedral group of order 2n (often the notation D n ...
Isomorphisms: 2 B 2 (2) is the Frobenius group of order 20. Remarks: Suzuki group are Zassenhaus groups acting on sets of size (2 2n+1) 2 + 1, and have 4-dimensional representations over the field with 2 2n+1 elements. They are the only non-cyclic simple groups whose order is not divisible by 3. They are not related to the sporadic Suzuki group.
Also included are groups in arts and entertainment (both fictional characters and performers or artists) and in history, and groups of abstract concepts. Criteria for inclusion: In order to be included in these lists, a group should be well known as a group, rather than being loosely associated people or concepts which happen to total to the ...
These groups (the groups of Lie type, together with the cyclic groups, alternating groups, and the five exceptional Mathieu groups) were believed to be a complete list, but after a lull of almost a century since the work of Mathieu, in 1964 the first Janko group was discovered, and the remaining 20 sporadic groups were discovered or conjectured ...
order of a group The order of a group (G, •) is the cardinality (i.e. number of elements) of G. A group with finite order is called a finite group. order of a group element The order of an element g of a group G is the smallest positive integer n such that g n = e. If no such integer exists, then the order of g is said to be infinite.
Groups of two persons (called by many names: dybs, pairs, couples, duos, etc.) are important either while standing alone or as building blocks of larger groupings. An infant requires a caregiver in order to survive, so life begins in a pair relationship that is apt to influence later ones.
In mathematics, the classification of finite simple groups (popularly called the enormous theorem [1] [2]) is a result of group theory stating that every finite simple group is either cyclic, or alternating, or belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six exceptions, called sporadic (the Tits group is sometimes regarded as a sporadic group ...
This list contains selected positive numbers in increasing order, including counts of things, ... (≈8.08 × 10 53) is the order of the monster group.