Geodesic
The strong reality and rationality of groups of unitriangular matrices of order $\le 8$ over fields of characteristic 2
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 71-83

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It is proved that an arbitrary matrix from the group of unitriangular matrices $UT_n(K)$, $n\le 8$, over an arbitrary field $K$ is conjugate in this group to a matrix whose commutativity graph is a forest. From this fact we derive the strong reality and rationality of the group $UT_n(K)$ for $n\le 8$ over an arbitrary field $K$ of characteristic 2.
Keywords: strong real group
Mots-clés : rational group, group of unitriangular matrices. 
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     title = {The strong reality and rationality of groups of unitriangular matrices of order $\le 8$ over fields of characteristic 2},
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O. A. Dubina; S. G. Kolesnikov; N. S. Managarova. The strong reality and rationality of groups of unitriangular matrices of order $\le 8$ over fields of characteristic 2. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 1, pp. 71-83. http://geodesic.mathdoc.fr/item/TIMM_2016_22_1_a7/