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Journal of Mathematical Sciences

, Volume 192, Issue 2, pp 250–262 | Cite as

Reduced Whitehead Groups and the Conjugacy Problem for Special Unitary Groups of Anisotropic Hermitian Forms

  • V. I. YanchevskiiEmail author
Article
  • 51 Downloads

Let K/k be a separable field extension of degree 2, D be a finite-dimensional central division algebra over K with a K/k-involution τ, h be an Hermitian anisotropic form on a right D-vector space with respect to τ, and let U(h) be the unitary group of h. Then the reduced Whitehead group of its special linear subgroup is defined as follows: \( \mathrm{SUK}_1^{\mathrm{an}}(h)={{{\mathrm{SU}(h)}} \left/ {{\left[ {U(h),U(h)} \right]}} \right.} \), where [U(h), U(h)] is the commutator subgroup of U(h). The first main result establishes a link between the above group and its analog SUK1(h) for the case of isotropic h (with respect to the same τ).

Theorem. There exists a surjective homomorphism from \( \mathrm{SUK}_1^{\mathrm{an}}(h) \) to SUK1(h).

Furthermore, we also give a solution of the conjugacy problem for special unitary subgroups of anisotropic Hermitian forms over quaternion division algebras as subgroups of their multiplicative groups. Bibliography: 32 titles.

Keywords

Unitary Group Field Extension Division Algebra Multiplicative Group Commutator Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute of Mathematics of the Belarus National Academy of SciencesMinskBelarus

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