Characterization of dilatations which are expressible as a product of three transvections or three reflections
Copyright policy )Characterization of dilatations which are expressible as a product of three transvections or three reflections
Let V V be a right vector space of dimension at least two over a division ring K K . We characterize the dilatations in GL ( V ) {\text {GL}}(V) which are expressible as a product of three transvections; these are precisely those dilatations whose ratio is a commutator. Similarly, if char K ≠ 2 K \ne 2 , a dilatation is a product of three reflections if and only if its ratio is a negative of a commutator. The sufficiency of these conditions was established earlier by B. B. Phadke.
Generators, relations, and presentations of groups, automorphisms, Matrices over special rings (quaternions, finite fields, etc.), division ring, vector space, commutator, Other matrix groups over fields, transvections, reflections, Factorization of matrices
Generators, relations, and presentations of groups, automorphisms, Matrices over special rings (quaternions, finite fields, etc.), division ring, vector space, commutator, Other matrix groups over fields, transvections, reflections, Factorization of matrices
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