Linearly pushforwardable automorphism

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This article defines an automorphism property related to (or which arises in the context of): linear representation theory
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This term is related to: Extensible automorphisms problem
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This is a variation of extensible automorphism|Find other variations of extensible automorphism |

Definition

Definition with symbols

Let G be a group and k be a field. An automorphism \sigma of G is termed linearly pushforwardable if for any linear representation \varphi:G \to GL_n(k), there exists a \in GL_n(k) such that for any g \in G, we have:

\varphi(\sigma(g)) = a\varphi(g)a^{-1}

Relation with other properties

Stronger properties

Weaker properties