publication . Article . Other literature type . 2015

Groups – Additive Notation

Roland Coghetto;
Open Access English
  • Published: 01 Jun 2015 Journal: Formalized Mathematics (issn: 1898-9934, Copyright policy)
  • Publisher: Sciendo
Abstract
<jats:title>Abstract</jats:title> <jats:p>We translate the articles covering group theory already available in the Mizar Mathematical Library from multiplicative into additive notation. We adapt the works of Wojciech A. Trybulec [41, 42, 43] and Artur Korniłowicz [25]. </jats:p> <jats:p>In particular, these authors have defined the notions of group, abelian group, power of an element of a group, order of a group and order of an element, subgroup, coset of a subgroup, index of a subgroup, conjugation, normal subgroup, topological group, dense subset and basis of a topological group. Lagrange’s theorem and some other theorems concerning these notions [9, 24, 22] a...
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doi: 10.1515/forma-2015-0013
Subjects
free text keywords: 20A05, 20K00, 03B35, additive group, subgroup, Lagrange theorem, conjugation, normal subgroup, index, additive topological group, basis, neighborhood, additive abelian group, Z-module, identifier: GROUP_1A, version: 8.1.045.32.1240, Mathematics, QA1-939, Discrete mathematics, G-module, Dicyclic group, Perfect group, Metabelian group, Alternating group, Coset, Quaternion group, Combinatorics
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