scholarly journals Classifying torsion-free subgroups of the Picard group

1984 ◽  
Vol 282 (1) ◽  
pp. 205-205 ◽  
Author(s):  
Andrew M. Brunner ◽  
Michael L. Frame ◽  
Youn W. Lee ◽  
Norbert J. Wielenberg
Keyword(s):  
Picard Group ◽  
Free Subgroups ◽  
Torsion Free

scholarly journals A family of conformally asymmetric Riemann surfaces

1997 ◽  
Vol 39 (2) ◽  
pp. 221-225 ◽  
Author(s):  
Brent Everitt
Keyword(s):  
Automorphism Group ◽  
Riemann Surfaces ◽  
Coset Diagrams ◽  
Free Subgroups ◽  
Torsion Free

AbstractWe give explicit examples of asymmetric Riemann surfaces (that is, Riemann surfaces with trivial conformal automorphism group) for all genera g ≥ 3. The technique uses Schreier coset diagrams to construct torsion-free subgroups in groups of signature (0; 2,3,r) for certain values of r.

ON A TORSION-FREE WEAKLY BRANCH GROUP DEFINED BY A THREE STATE AUTOMATON

2002 ◽  
Vol 12 (01n02) ◽  
pp. 223-246 ◽  
Author(s):  
ROSTISLAV I. GRIGORCHUK ◽  
ANDRZEJ ŻUK
Keyword(s):  
Forthcoming Paper ◽  
Galois Groups ◽  
Branch Group ◽  
Free Subgroups ◽  
Torsion Free

We study a torsion free weakly branch group G without free subgroups defined by a three state automaton which appears in different problems related to amenability, Galois groups and monodromy. Here and in the forthcoming paper [20] we establish several important properties of G related to fractalness, branchness, just infinitness, growth, amenability and presentations.

scholarly journals Torsion free subgroups of fuchsian groups and tessellations of surfaces

1982 ◽  
Vol 69 (3) ◽  
pp. 331-346 ◽  
Author(s):  
Allan L. Edmonds ◽  
John H. Ewing ◽  
Ravi S. Kulkarni
Keyword(s):  
Fuchsian Groups ◽  
Free Subgroups ◽  
Torsion Free

Free Subgroups and the Residual Nilpotence of the Group of Units of Modular and p-Adic Group Rings

1986 ◽  
Vol 29 (3) ◽  
pp. 321-328 ◽  
Author(s):  
Jairo Zacarias Gonçalves
Keyword(s):  
Finite Group ◽  
Commutative Ring ◽  
Group Rings ◽  
Characteristic P ◽  
Prime Field ◽  
Torsion Free Group ◽  
Group Of Units ◽  
Residual Nilpotence ◽  
Free Subgroups ◽  
Torsion Free

AbstractLet G be a group, let RG be the group ring of the group G over the unital commutative ring R and let U(RG) be its group of units. Conditions which imply that U(RG) contains no free noncyclic group are studied, when R is a field of characteristic p ≠ 0, not algebraic over its prime field, and G is a solvable-by-finite group without p-elements. We also consider the case R = ℤp, the ring of p-adic integers and G torsionby- nilpotent torsion free group. Finally, the residual nilpotence of U(ℤpG) is investigated.

scholarly journals Unique product groups and congruence subgroups

2020 ◽  
pp. 2250025
Author(s):  
Will Craig ◽  
Peter A. Linnell
Keyword(s):  
Congruence Subgroups ◽  
Unique Product ◽  
Normal Series ◽  
Free Subgroups ◽  
Torsion Free

We prove that a uniform pro-[Formula: see text] group with no non-abelian free subgroups has a normal series with torsion-free abelian factors. We discuss this in relation to unique product groups. We also consider generalizations of Hantzsche–Wendt groups.

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