Geodesic
Involutions of the general linear group $GL_2$ over a subring of the field~$\mathbb{Q}$
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 62 (2019), pp. 19-26

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The necessary and sufficient conditions for the conjugacy of involutions of the group $GL_2$ over an arbitrary subring of the field $\mathbb{Q}$ are obtained. It is shown that if this subring is (not) $2$-divisible, then the number of classes of conjugate off-center involutions is $1$ (respectively $2$).
Mots-clés : matrix
Keywords: general linear group, conjugate involutions, inner automorphism. 
@article{VTGU_2019_62_a1,
     author = {V. A. Gaidak and E. A. Timoshenko},
     title = {Involutions of the general linear group $GL_2$ over a subring of the field~$\mathbb{Q}$},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {19--26},
     publisher = {mathdoc},
     number = {62},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2019_62_a1/}
}
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V. A. Gaidak; E. A. Timoshenko. Involutions of the general linear group $GL_2$ over a subring of the field~$\mathbb{Q}$. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 62 (2019), pp. 19-26. http://geodesic.mathdoc.fr/item/VTGU_2019_62_a1/