Complete map

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Revision as of 23:39, 21 January 2009 by Vipul (talk | contribs) (New page: {{semistddef}} ==Definition== A '''complete map''' from a group <math>G</math> to itself is a bijection <math>\varphi:G \to G</math> such that the map <math>g \mapsto g \varphi(g)</math>...)
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This article defines a term that has been used or referenced in a journal article or standard publication, but may not be generally accepted by the mathematical community as a standard term.[SHOW MORE]

Definition

A complete map from a group G to itself is a bijection \varphi:G \to G such that the map g \mapsto g \varphi(g) is also a bijection.

Note that if \alpha is an automorphism of G, the map g \mapsto \alpha(g^{-1}) is a complete map if and only if \alpha is a fixed-point-free automorphism.

Facts