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articleNo Access
Conjugate real classes in general linear groups
Journal of Algebra and Its Applications01 Mar 2019
Preview Abstract
Let $F$ $F$ be a field with a nontrivial involution $c : α \mapsto α^{c}$ $c : α \mapsto α^{c}$ . An element $g \in {GL}_{n} (F)$ $g \in {GL}_{n} (F)$ is called $c$ $c$ -real if it is conjugate to ${(g^{c})}^{- 1}$ ${(g^{c})}^{- 1}$ . We prove that for $n \geq 2$ $n \geq 2$ , $g \in {GL}_{n} (F)$ $g \in {GL}_{n} (F)$ is $c$ $c$ -real if and only if it has a representation in some unitary group of degree $n$ $n$ over $F$ $F$ .

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