Section (group theory)
Encyclopedia
In group theory
a section of a group G is a group that is, or is isomorphic to, a quotient group
of a subgroup
of G.
s, 20 are sections of the monster group
, and are referred to as the "Happy Family".
Group theory
In mathematics and abstract algebra, group theory studies the algebraic structures known as groups.The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces can all be seen as groups endowed with additional operations and...
a section of a group G is a group that is, or is isomorphic to, a quotient group
Quotient group
In mathematics, specifically group theory, a quotient group is a group obtained by identifying together elements of a larger group using an equivalence relation...
of a subgroup
Subgroup
In group theory, given a group G under a binary operation *, a subset H of G is called a subgroup of G if H also forms a group under the operation *. More precisely, H is a subgroup of G if the restriction of * to H x H is a group operation on H...
of G.
Examples
Of the 26 sporadic groupSporadic group
In the mathematical field of group theory, a sporadic group is one of the 26 exceptional groups in the classification of finite simple groups. A simple group is a group G that does not have any normal subgroups except for the subgroup consisting only of the identity element, and G itself...
s, 20 are sections of the monster group
Monster group
In the mathematical field of group theory, the Monster group M or F1 is a group of finite order:...
, and are referred to as the "Happy Family".