Graphs and block designs associated with the three-dimensional unitary groups

1974 ◽  
pp. 128-131 ◽  
Author(s):  
D. E. Taylor
Keyword(s):  
Three Dimensional ◽  
Unitary Groups ◽  
Block Designs

scholarly journals Vertical Distribution Relations for Special Cycles on Unitary Shimura Varieties

2018 ◽  
Vol 2020 (13) ◽  
pp. 3902-3926
Author(s):  
Réda Boumasmoud ◽  
Ernest Hunter Brooks ◽  
Dimitar P Jetchev
Keyword(s):  
Vertical Distribution ◽  
Three Dimensional ◽  
Complex Multiplication ◽  
Horizontal Distribution ◽  
Unitary Groups ◽  
Shimura Varieties ◽  
Heegner Points ◽  
Universal Norm

Abstract We consider cycles on three-dimensional Shimura varieties attached to unitary groups, defined over extensions of a complex multiplication (CM) field $E$, which appear in the context of the conjectures of Gan et al. [6]. We establish a vertical distribution relation for these cycles over an anticyclotomic extension of $E$, complementing the horizontal distribution relation of [8], and use this to define a family of norm-compatible cycles over these fields, thus obtaining a universal norm construction similar to the Heegner $\Lambda $-module constructed from Heegner points.

scholarly journals Short Presentations for Three-Dimensional Unitary Groups

2001 ◽  
Vol 245 (2) ◽  
pp. 719-729 ◽  
Author(s):  
Alexander Hulpke ◽  
Ákos Seress
Keyword(s):  
Three Dimensional ◽  
Unitary Groups

Three-Dimensional Incomplete Block Designs for Interaction Models

Biometrics ◽  
1963 ◽  
Vol 19 (2) ◽  
pp. 229
Author(s):  
Richard F. Potthoff
Keyword(s):  
Three Dimensional ◽  
Block Designs ◽  
Incomplete Block ◽  
Interaction Models

scholarly journals Flag-transitive block designs and unitary groups

2020 ◽  
Vol 193 (3) ◽  
pp. 535-553
Author(s):  
Seyed Hassan Alavi ◽  
Mohsen Bayat ◽  
Ashraf Daneshkhah
Keyword(s):  
Unitary Groups ◽  
Block Designs

scholarly journals On groups generated by three-dimensional special unitary groups I

1977 ◽  
Vol 23 (1) ◽  
pp. 67-77 ◽  
Author(s):  
Kok-Wee Phan
Keyword(s):  
Unitary Group ◽  
Three Dimensional ◽  
Unitary Groups ◽  
Linear Groups ◽  
Direct Sum ◽  
Underlying Space ◽  
Carry Over

This paper is the result of our attempt to carry over the method of our characterization of the linear groups PSL(n, q) (Phan (1972)) to that of the unitary groups PSU (n, q). It appears desirable to have available a result on the generation of the unitary groups more closely related to the splitting of the underlying hermitian spaces of these groups into orthogonal direct sum of anisotropic lines. Another motivation comes also from our work on the unitary groups in which we obtained a fusion pattern different from that of the unitary group when the dimension of the underlying space is eight. This fusion pattern produces a group whose structure is not immediately apparent. In order to identify this group, the result of this paper appears to be a necessary step.

scholarly journals On groups generated by three-dimensional special unitary groups II

1977 ◽  
Vol 23 (2) ◽  
pp. 129-146 ◽  
Author(s):  
Kok-Wee Phan
Keyword(s):  
Recent Result ◽  
Three Dimensional ◽  
Unitary Groups ◽  
Direct Approach ◽  
Universal Group ◽  
Type D

We shall determine in this paper groups of types Dn, E6, E7 and E8 generated by SU(3, q)'s, q odd, q > 3. These groups are defined in Phan (1975). [We shall refer to this paper as I]. Acquaintance with the results of I is assumed. The identification of groups of type D4 is similar to that of SU(n, q). We actually construct an isomorphism from the universal group of type D4 onto Spin+(8, q). This direct approach does not appear to be feasible for groups of type Dn with n ≧ 5. Fortunately Wong's recent result (1974) is applicable here. But his theorem requires that the characteristic of the field be odd; hence unlike the unitary case, we assume that q is odd and q 3. Using Wong's theorem, we proceed to show by induction that groups of type Dn are homomorphic images of Spin+(2n, q) or Spin −(2n, q) according as n is even or n is odd.

scholarly journals Correction to: Flag-transitive block designs and unitary groups

2021 ◽  
Author(s):  
Seyed Hassan Alavi ◽  
Mohsen Bayat ◽  
Ashraf Daneshkhah
Keyword(s):  
Unitary Groups ◽  
Block Designs

Visuospatial, Visuoperceptual, and Visuoconstructive Abilities in Congenital Hypothyroidism

2013 ◽  
Vol 19 (10) ◽  
pp. 1119-1127 ◽  
Author(s):  
Nevena Simic ◽  
Sarah Khan ◽  
Joanne Rovet
Keyword(s):  
Congenital Hypothyroidism ◽  
Three Dimensional ◽  
Thyroid Stimulating Hormone ◽  
Self Report ◽  
Block Designs ◽  
Typically Developing ◽  
Sense Of Direction ◽  
Profile View ◽  
Abstract Shapes ◽  
Tsh Levels

AbstractIndividuals with congenital hypothyroidism (CH), even those diagnosed and treated early, experience selective cognitive deficits, the most striking of which involves the visuocognitive domain. However, the range and nature of their visuocognitive disturbances is not fully understood. We assessed a range of higher-order visuocognitive abilities in 19 children and adolescents with CH and 19 age- and sex-matched typically developing peers (TD) using a battery of neuropsychological tests and a novel self-report measure of sense of direction. CH scored lower than TD on direct tests of visuocognitive function (judging line orientation, parts-to-whole localization, copying three-dimensional block towers, discriminating designs, and matching unfamiliar faces in ¾ profile-view) as well as on self-reported problems in spatial ability. Visuocognitive problems were not global as CH and TD did not differ at copying two-dimensional block designs, mentally rotating and matching abstract shapes, or at matching unfamiliar front-view faces, design features, or designs that engaged either figure-ground segregation, visual constancy, or closure. Early and concurrent thyroid stimulating hormone (TSH) levels were associated with visuocognitive ability, although attention and working memory were not. Individuals with CH exhibit selective visuocognitive weaknesses, some of which are related to early and concurrent TSH levels. (JINS, 2013, 19, 1–9)

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