Overdiagonal subgroups of the hyperbolic unitary group for a good form ring over a field

1999 ◽  
Vol 95 (2) ◽  
pp. 2096-2101 ◽  
Author(s):  
E. V. Dybkova
Keyword(s):  
Unitary Group ◽  
Form Ring ◽  
Hyperbolic Unitary Group

Stable sandwich classification theorem for classical-like groups

2007 ◽  
Vol 143 (3) ◽  
pp. 607-619 ◽  
Author(s):  
ZUHONG ZHANG
Keyword(s):  
Unitary Group ◽  
Classification Theorem ◽  
Stable Case ◽  
Form Ring ◽  
Image Position

AbstractLet H denote a subgroup of the unitary group U(R, Λ) which is normalized by EU(J, ΓJ) for some form ideal (J, ΓJ) of a commutative form ring (R, Λ). We prove that H satisfies a “sandwich” property, i.e., there exists a form ideal (I ΓI) such that for some form ideal (I : J7, Ω). This answers a conjecture of Bak (1967) in the stable case.

scholarly journals The subnormal structure of classical-like groups over commutative rings

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Raimund Preusser
Keyword(s):  
Unitary Group ◽  
Hermitian Form ◽  
Commutative Rings ◽  
Unitary Groups ◽  
Elementary Subgroup ◽  
Sandwich Theorem ◽  
Subnormal Structure ◽  
Form Ring ◽  
K 12 ◽  
Subnormal Subgroups

AbstractLet 𝑛 be an integer greater than or equal to 3, and let (R,\Delta) be a Hermitian form ring, where 𝑅 is commutative. We prove that if 𝐻 is a subgroup of the odd-dimensional unitary group \operatorname{U}_{2n+1}(R,\Delta) normalised by a relative elementary subgroup \operatorname{EU}_{2n+1}((R,\Delta),(I,\Omega)), then there is an odd form ideal (J,\Sigma) such that\operatorname{EU}_{2n+1}((R,\Delta),(JI^{k},\Omega_{\mathrm{min}}^{JI^{k}}\dotplus\Sigma\circ I^{k}))\leq H\leq\operatorname{CU}_{2n+1}((R,\Delta),(J,\Sigma)),where k=12 if n=3 respectively k=10 if n\geq 4. As a consequence of this result, we obtain a sandwich theorem for subnormal subgroups of odd-dimensional unitary groups.

scholarly journals Structure of Hyperbolic Unitary Groups II: Classification of E-Normal Subgroups

2017 ◽  
Vol 24 (02) ◽  
pp. 195-232 ◽  
Author(s):  
Raimund Preusser
Keyword(s):  
Unitary Group ◽  
Direct Limit ◽  
Finite Ring ◽  
Unitary Groups ◽  
Normal Subgroups ◽  
Finite Rings ◽  
Elementary Subgroup ◽  
Rings With Involution ◽  
Hyperbolic Unitary Group

This paper proves the sandwich classification conjecture for subgroups of an even dimensional hyperbolic unitary group [Formula: see text] which are normalized by the elementary subgroup [Formula: see text], under the condition that R is a quasi-finite ring with involution, i.e., a direct limit of module finite rings with involution, and [Formula: see text].

Crystal Structure and Conformation of Ring A of 2β-Bromo-19β,28-epoxy-18α-oleanan-3-one

1993 ◽  
Vol 58 (11) ◽  
pp. 2737-2744 ◽  
Author(s):  
Jiří Novotný ◽  
Jaroslav Podlaha ◽  
Jiří Klinot
Keyword(s):  
Crystal Structure ◽  
Opposite Direction ◽  
Chair Conformation ◽  
Boat Conformation ◽  
Form Ring ◽  
Twist Boat

The crystal structure of β-bromo-19β,28-epoxy-18α-oleanan-3-one was elucidated. The crystal is orthorhombic, P212121, a = 9.686(1), b = 14.355(2), c = 19.687(4) Å, Z = 4, R = 0.042 for 2 410 observed reflections. Rings B, C, D and E adopt the chair conformation, the five membered ether cycle in ring E occurs in the envelope form. Ring A takes the twist-boat conformation turned towards the classical boat with C2 and C5 in the stem-stern position, in contrast to the conformation in solution, which is turned in the opposite direction towards the classical boat with C3 and C10 in the stem-stern positions.

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