The Linearity Problem for the Unitriangular Automorphism Groups of Free Groups
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https://elib.sfu-kras.ru/handle/2311/10083Author:
Roman’kov, Vitaly A.
Романьков, Виталий А.
Date:
2013-11Abstract:
We prove that the unitriangular automorphism group of a free group of rank n has a faithful representation
by matrices over a field, or in other words, it is a linear group, if and only if n 3. Thus, we have
completed a description of relatively free groups with linear the unitriangular automorphism groups. This
description was initiated by Erofeev and the author in [1], where proper varieties of groups have been
considered Доказано, что группа унитреугольных автоморфизмов свободной группы ранга n допускает точное представление матрицами над полем тогда и только тогда, когда n 6 3. Таким образом
завершено описание относительно свободных групп, группы унитреугольных автоморфизмов которых линейны, начатое работой С. Ю. Ерофеева и автора [1] , где рассмотрены все относительно свободные группы собственных многообразий групп
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