Groups and their Subgroups

E. S. Lyapin, A. Ya. Aizenshtat and M. M. Lesokhin

Chapter Chapter 4 in Exercises in Group Theory, 1972, pp 79-105 from Springer

Abstract: Abstract Let H be a subgroup of a group G,x ∈; G. The set xH is called a right coset of H in G, and Hx is called a left coset of H in G. If G is written as the union of its mutually disjoint right cosets of H: 1 $$ G = x_\alpha H \cup x_\beta H \cup \ldots \cup x_ \in H \cup \ldots $$ then such a partition is called the right decomposition of G by H. The set {xα,xβ,…,xξ,…} is called the set of representatives of the right decomposition of G byH.

Keywords: Normal Subgroup; Finite Group; Conjugate Classis; Symmetric Group; Factor Group (search for similar items in EconPapers)
Date: 1972
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DOI: 10.1007/978-1-4613-4589-3_4

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