Distances in Algebra

Michel Marie Deza and Elena Deza
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Michel Marie Deza: Ecole Normale Supérieure
Elena Deza: Moscow State Pedagogical University

Chapter Chapter 10 in Encyclopedia of Distances, 2016, pp 199-214 from Springer

Abstract: Abstract A group (G, ⋅ , e) is a set G of elements with a binary operation ⋅ , called the group operation, that together satisfy the four fundamental properties of closure (x ⋅ y ∈ G for any x, y ∈ G), associativity (x ⋅ (y ⋅ z) = (x ⋅ y) ⋅ z for any x, y, z ∈ G), the identity property ( $$x \cdot e = e \cdot x = x$$ for any x ∈ G), and the inverse property (for any x ∈ G, there exists an element x −1 ∈ G such that $$x \cdot x^{-1} = x^{-1} \cdot x = e$$ ).

Keywords: Group Norm; Cayley Graph; Banach Lattice; Riesz Space; Carnot Group (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/978-3-662-52844-0_10

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