Geodesic
$\mathscr H$-bijections of groups and $\mathscr H_R$-isomorphisms of group rings
Sbornik. Mathematics, Tome 188 (1997) no. 6, pp. 823-841 Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce and investigate the notions indicated in the title. In particular, as an application, we prove the conjecture on the finiteness of the automorphism group of an orthogonal decomposition of an associative algebra, for all known examples of orthogonal decompositions. 
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     title = {$\mathscr H$-bijections of groups and $\mathscr H_R$-isomorphisms of group rings},
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D. N. Ivanov. $\mathscr H$-bijections of groups and $\mathscr H_R$-isomorphisms of group rings. Sbornik. Mathematics, Tome 188 (1997) no. 6, pp. 823-841. http://geodesic.mathdoc.fr/item/SM_1997_188_6_a1/

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