Geodesic
Representations of dihedral groups over a~field of characteristic~2
Sbornik. Mathematics, Tome 25 (1975) no. 1, pp. 58-68

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In this paper there is given a complete classification of the representations of the group $(2)*(2)$ (where $*$ denotes the free product) and the finite dihedral groups over a field of characteristic 2. These results follow from the solution of the problem of classifying to within similarity pairs of matrices $A,B$ (over a field) for which $A^2=0$, $B^2=0$. Bibliography: 5 titles. 
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     title = {Representations of dihedral groups over a~field of characteristic~2},
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V. M. Bondarenko. Representations of dihedral groups over a~field of characteristic~2. Sbornik. Mathematics, Tome 25 (1975) no. 1, pp. 58-68. http://geodesic.mathdoc.fr/item/SM_1975_25_1_a2/