Schreier Coset Graph
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High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In the area of mathematics called combinatorial group theory, the Schreier coset graph is a graph associated to a group G, a generating set { xi : i in I }, and a subgroup H G. The vertices of the graph are the right cosets Hg = { hg : h in G } for g in G. The edges of the graph are of the form (Hg,Hgxi). The Cayley graph of the group G with { xi : i in I } is the Schreier coset graph for H = { 1G }. The graph is named after Otto Schreier. The graph is useful to understand coset enumeration and the Todd Cox...
High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In the area of mathematics called combinatorial group theory, the Schreier coset graph is a graph associated to a group G, a generating set { xi : i in I }, and a subgroup H G. The vertices of the graph are the right cosets Hg = { hg : h in G } for g in G. The edges of the graph are of the form (Hg,Hgxi). The Cayley graph of the group G with { xi : i in I } is the Schreier coset graph for H = { 1G }. The graph is named after Otto Schreier. The graph is useful to understand coset enumeration and the Todd Coxeter algorithm. A spanning tree of a Schreier coset graph corresponds to a Schreier transversal, as in Schreier's subgroup lemma, (Conder 2003). Coset graphs can be used to form large permutation representations of groups and were used by Graham Higman to show that the alternating groups of large enough degree are Hurwitz groups, (Conder 2003).
