Results 121 to 130 of about 116,933 (156)

Fuchsian Subgroups of the Picard Group

Canadian Journal of Mathematics, 1976
The Picard group Γ = PSL2 (Z(i)) is the group of linear transformationswith a, b, c, d Gaussian integers.Γ is of interest both as an abstract group and in automorphic function theory [10]. In [10] Waldinger constructed a subgroup H of finite index which is a generalized free product, while in [1] Fine showed that T is a semidirect product with the ...
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The Group of Outer Automorphisms and the Picard Group of an Algebra

Algebras and Representation Theory, 1999
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Guil-Asensio, Francisco, Saorín, Manuel
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Congruence Subgroups of the Picard Group

Canadian Journal of Mathematics, 1980
The Picard group Γ = PSL2 (Z [i]) is the group of linear fractional transformationswith ad – bc = ± 1 and a, b, c, d Gaussian integers.Γ is of interest as an abstract group and in automorphic function theory. In an earlier paper [1], a decomposition of Γ as a free product with amalgamated subgroup was given and this was utilized to investigate Fuchsian
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The normaliser of the modular group in the Picard group

2000
The well-known modular group \(M=\text{PSL}(2,\mathbb{Z})\) is a subgroup of the Picard group \(\text{PSL}(2,\mathbb{Z}[i])\). As it is a non-normal subgroup, it had been an interesting problem to find its normalizer. The authors obtain the normalizer of the modular group \(M\) in \(P\) as \(S_3*_{\mathbb{Z}_2}D_2\), i.e.
Cangül, İsmail Naci, Yılmaz Özgür, Nihal   +1 more
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Grothendieck Groups and Picard Groups of Abelian Group Rings

The Annals of Mathematics, 1967
For a commutative ring A we study here the Grothendieck group, K0A, of finitely generated projective A-modules, and the Picard group, Pic (A), of projective modules of rank one (under (?A). Writing koA for the elements of rank zero in KOA, there is an epimorphism det: K0A Pic (A) defined by the rth exterior power of a projective module of rank r.
Bass, H., Murthy, M. P.
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On the hermitian picard group of a congruence order

Communications in Algebra, 1996
In this note methods are developed which permit us to concretely calculate the hermitian Picard group of a congruence order A over a discrete valuation ring, with respect to an involution α of A. In particular, this allows us to exhibit some explicit examples of algebras A whose hermitian Picard group strongly depends upon the chosen involution on A.
Verhaeghe, Pieter, Verschoren, Alain
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On the local Picard group

Proceedings of the Steklov Institute of Mathematics, 2009
The aim of this paper is to prove local Lefschetz theorems for the Picard groups of a complex singularity \((X,0)\). These are obtained by imposing conditions on the depth of the corresponding `link' \(X\setminus \{0\}\) and also on the rectified cohomological depth of a generic hyperplane complement \(X \setminus H\).
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Class Groups and Picard Groups of Orders

Proceedings of the London Mathematical Society, 1974
Fröhlich, A., Reiner, Irving, Ullom, S.
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The Picard group of a monoid domain, II

Archiv der Mathematik, 1990
[For part I see J. Algebra 115, No.2, 342-351 (1988; Zbl 0651.13009).] Let R be an integral domain and S a nonzero commutative cancellative torsion-free monoid with group of invertible elements H properly contained in S. Then \(Pic(R[H])=Pic(R[S])\) if and only if R[S] is seminormal. This generalizes part I of this work.
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On The Picard Group of An Abelian Group Ring

1986
Publisher Summary This chapter discusses the Picard group of an abelian group ring surveys results relating the Picard group of a ring A to that of the ring A (G) for G a free abelian monoid or group. Swan has shown that, if G is a free abelian monoid, then the factor group Pic (A [G])/Pic (A) vanishes only if A/(nil A) is a seminormal ring. Bass and
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