TY - JOUR

T1 - Overgroups of Elementary Block Diagonal Subgroups in Even Unitary Groups over Quasi-Finite Rings: Main Results

AU - Shchegolev, A.V.

PY - 2017

Y1 - 2017

N2 - © 2017 Springer Science+Business Media New YorkLet H be a subgroup of the hyperbolic unitary group U(2n,R, Λ) that contains an elementary block diagonal subgroup EU(ν, R, Λ) of type ν. Assume that all self-conjugate blocks of EU(ν, R, Λ) are of size at least 6 (at least 4 if the form parameter Λ satisfies the condition RΛ+ΛR = R) and that all non-self-conjugate blocks are of size at least 5. Then there exists a unique major exact form net of ideals (σ, Γ) such that EU(σ, Γ) ≤ H ≤ NU(2n,R,Λ)(U(σ, Γ)), where NU(2n,R,Λ)(U(σ, Γ)) stands for the normalizer in U(2n,R, Λ) of the form net subgroup U(σ, Γ) of level (σ, Γ) and EU(σ, Γ) denotes the corresponding elementary form net subgroup. The normalizer NU(2n,R,Λ)(U(σ, Γ)) is described in terms of congruences.

AB - © 2017 Springer Science+Business Media New YorkLet H be a subgroup of the hyperbolic unitary group U(2n,R, Λ) that contains an elementary block diagonal subgroup EU(ν, R, Λ) of type ν. Assume that all self-conjugate blocks of EU(ν, R, Λ) are of size at least 6 (at least 4 if the form parameter Λ satisfies the condition RΛ+ΛR = R) and that all non-self-conjugate blocks are of size at least 5. Then there exists a unique major exact form net of ideals (σ, Γ) such that EU(σ, Γ) ≤ H ≤ NU(2n,R,Λ)(U(σ, Γ)), where NU(2n,R,Λ)(U(σ, Γ)) stands for the normalizer in U(2n,R, Λ) of the form net subgroup U(σ, Γ) of level (σ, Γ) and EU(σ, Γ) denotes the corresponding elementary form net subgroup. The normalizer NU(2n,R,Λ)(U(σ, Γ)) is described in terms of congruences.

U2 - 10.1007/s10958-017-3319-2

DO - 10.1007/s10958-017-3319-2

M3 - статья

VL - 222

SP - 516

EP - 523

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 4

ER -