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In mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group. Let be a finitely generated group. Then, for each integer define to be the number of subgroups of index in . Similarly, if is a topological group, denotes the number of open subgroups of index in . One similarly defines and to denote the number of maximal and normal subgroups of index , respectively. Subgroup growth studies these functions, their interplay, and the characterization of group theoretical properties in terms of these functions.

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  • In mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group. Let be a finitely generated group. Then, for each integer define to be the number of subgroups of index in . Similarly, if is a topological group, denotes the number of open subgroups of index in . One similarly defines and to denote the number of maximal and normal subgroups of index , respectively. Subgroup growth studies these functions, their interplay, and the characterization of group theoretical properties in terms of these functions. The theory was motivated by the desire to enumerate finite groups of given order, and the analogy with Mikhail Gromov's notion of word growth. (en)
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  • In mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group. Let be a finitely generated group. Then, for each integer define to be the number of subgroups of index in . Similarly, if is a topological group, denotes the number of open subgroups of index in . One similarly defines and to denote the number of maximal and normal subgroups of index , respectively. Subgroup growth studies these functions, their interplay, and the characterization of group theoretical properties in terms of these functions. (en)
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  • Subgroup growth (en)
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