Results 1 to 10 of about 5,046 (150)
On the finite index subgroups of Houghton’s groups [PDF]
Archiv der Mathematik, 2022 AbstractHoughton’s groups $$H_2, H_3, \ldots $$ H 2 , H 3 , … are ...
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FINITE INDEX SUBGROUPS OF FULLY RESIDUALLY FREE GROUPS [PDF]
International Journal of Algebra and Computation, 2011 Using graph-theoretic techniques for f.g. subgroups of Fℤ[t]we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked effectively. As an application we obtain an analogue of Greenberg–Stallings Theorem for f.g. fully residually free groups, and prove that
Nikolaev, Andrey V., Serbin, Denis E.
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Multiplicative subgroups of finite index in a ring [PDF]
Proceedings of the American Mathematical Society, 1992 If G G is a subgroup of finite index in the multiplicative group of an infinite field K K then G − G = K G - G = K . Similar results hold for various rings.
Bergelson, Vitaly, Shapiro, Daniel B.
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Subgroups of finite index in nilpotent groups
Inventiones Mathematicae, 1988 ``A finitely generated group has only a finite number of subgroups of each finite index. How does this number vary with the index?'' Thus the authors introduce this beautiful paper. The question is tackled for finitely generated torsion-free nilpotent groups, referred to as \({\mathcal T}\)-groups, via the zeta function associated to the arithmetical ...
Grunewald, F.J., Segal, D., Smith, G.C.
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Subgroups of finite index in profinite groups [PDF]
Pacific Journal of Mathematics, 1976 A profinite group is called strongly complete if every subgroup of finite index is open and of type (AF) if it has only finitely many subgroups of any fixed index. In this paper it is shown that a topologically finitely generated abelian by pro-nilpotent profinite group is strongly complete, and that a pro-solvable profinite group is strongly complete ...
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Commensurations and subgroups of finite index of Thompson’s groupF [PDF]
Geometry & Topology, 2008 We determine the abstract commensurator Com. F/ of Thompson's group F and describe it in terms of piecewise linear homeomorphisms of the real line. We show Com. F/ is not finitely generated and determine which subgroups of finite index in F are isomorphic to F.
Burillo, José +2 more
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On finite-index extensions of subgroups of free groups [PDF]
Journal of Group Theory, 2010 We study the lattice of finite-index extensions of a given finitely generated subgroup $H$ of a free group $F$. This lattice is finite and we give a combinatorial characterization of its greatest element, which is the commensurator of $H$. This characterization leads to a fast algorithm to compute the commensurator, which is based on a standard ...
Silva, Pedro, Weil, Pascal
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Finite index subgroups of mapping class groups [PDF]
Proceedings of the London Mathematical Society, 2013 Let $g\geq3$ and $n\geq0$, and let ${\mathcal{M}}_{g,n}$ be the mapping class group of a surface of genus $g$ with $n$ boundary components. We prove that ${\mathcal{M}}_{g,n}$ contains a unique subgroup of index $2^{g-1}(2^{g}-1)$ up to conjugation, a unique subgroup of index $2^{g-1}(2^{g}+1)$ up to conjugation, and the other proper subgroups of ...
Berrick, A.J., Gebhardt, V., Paris, L.
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Subgroups of Finite Index in a Free Product With Amalgamated Subgroup [PDF]
Mathematics of Computation, 1981 Let G be a free product of finitely many finite groups with amalgamated subgroup. Using coset diagrams, a recurrence relation is obtained for the number of subgroups, and of free subgroups, of each finite index in G. In the latter case, an asymptotic formula is derived. When the amalgamated subgroup is central, the relation takes a simpler form.
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On subgroups of finite index in branch groups
Journal of Algebra, 2014 We give a structural description of the normal subgroups of subgroups of finite index in branch groups in terms of rigid stabilizers. This gives further insight into the structure lattices of branch groups introduced by the second author. We derive a condition concerning abstract commensurability of branch groups acting on the p-ary tree for any prime ...
Garrido, Alejandra, Wilson, John S.
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