Plane and layer symmetry groups
S. V. Jablan (1990)
Matematički Vesnik
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S. V. Jablan (1990)
Matematički Vesnik
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Michael Larsen, Alexander Lubotzky, Claude Marion (2014)
Journal of the European Mathematical Society
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Let with and let be the corresponding hyperbolic triangle group. Many papers have been dedicated to the following question: what are the finite (simple) groups which appear as quotients of ? (Classically, for and more recently also for general .) These papers have used either explicit constructive methods or probabilistic ones. The goal of this paper is to present a new approach based on the theory of representation varieties (via deformation theory). As a corollary we essentially...
S. V. Jablan (1990)
Matematički Vesnik
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Marco Marchi (2014)
Annales de l’institut Fourier
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In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano...
Daniel Smertnig (2010)
Colloquium Mathematicae
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For a finite abelian group G and a splitting field K of G, let (G,K) denote the largest integer l ∈ ℕ for which there is a sequence over G such that for all . If (G) denotes the Davenport constant of G, then there is the straightforward inequality (G) - 1 ≤ (G,K). Equality holds for a variety of groups, and a conjecture of W. Gao et al. states that equality holds for all groups. We offer further groups for which equality holds, but we also give the first examples of groups G for...
Robert Guralnick, Pham Tiep (2012)
Journal of the European Mathematical Society
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The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi–Yau varieties. In this paper, we solve a problem raised by J. Kollár and M. Larsen on the structure of finite irreducible linear groups generated by elements of age . More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation....
Martin Liebeck, Dan Segal, Aner Shalev (2012)
Journal of the European Mathematical Society
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For a group and a positive real number , define to be the number of integers less than which are dimensions of irreducible complex representations of . We study the asymptotics of for algebraic groups, arithmetic groups and finitely generated linear groups. In particular we prove an “alternative” for finitely generated linear groups in characteristic zero, showing that either there exists such that for all large , or is virtually abelian (in which case is bounded). ...
Olga Kharlampovich, Alexei Myasnikov (2012)
Journal of the European Mathematical Society
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We describe finitely generated groups universally equivalent (with constants from in the language) to a given torsion-free relatively hyperbolic group with free abelian parabolics. It turns out that, as in the free group case, the group embeds into the Lyndon’s completion of the group , or, equivalently, embeds into a group obtained from by finitely many extensions of centralizers. Conversely, every subgroup of containing is universally equivalent to . Since finitely...
Huaguo Shi, Zhangjia Han, Guiyun Chen (2012)
Colloquium Mathematicae
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Let G be a finite group, and (p ≥ 3). It is proved that G ≅ M if G and M have the same order components.
Laurent Bartholdi, Anna Erschler (2014)
Annales de l’institut Fourier
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We show that there exists a finitely generated group of growth for all functions satisfying for all large enough and the positive root of . Set ; then all functions that grow uniformly faster than are realizable as the growth of a group. We also give a family of sum-contracting branched groups of growth for a dense set of .
Giovanni Felder, A. Veselov (2005)
Journal of the European Mathematical Society
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We consider both standard and twisted actions of a (real) Coxeter group on the complement to the complexified reflection hyperplanes by combining the reflections with complex conjugation. We introduce a natural geometric class of special involutions in and give explicit formulae which describe both actions on the total cohomology in terms of these involutions. As a corollary we prove that the corresponding twisted representation is regular only for the symmetric group , the...
Eike Lau (2009)
Annales scientifiques de l'École Normale Supérieure
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We show that the Zink equivalence between -divisible groups and Dieudonné displays over a complete local ring with perfect residue field of characteristic is compatible with duality. The proof relies on a new explicit formula for the -divisible group associated to a Dieudonné display.
Ionut Chifan, Thomas Sinclair (2013)
Annales scientifiques de l'École Normale Supérieure
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Ozawa showed in [21] that for any i.c.c. hyperbolic group, the associated group factor is solid. Developing a new approach that combines some methods of Peterson [29], Ozawa and Popa [27, 28], and Ozawa [25], we strengthen this result by showing that is strongly solid. Using our methods in cooperation with a cocycle superrigidity result of Ioana [12], we show that profinite actions of lattices in , , are virtually -superrigid.
Brunetto Piochi (1989)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Let be a group and be an integer greater than or equal to . is said to be -permutable if every product of elements can be reordered at least in one way. We prove that, if has a centre of finite index , then is -permutable. More bounds are given on the least such that is -permutable.
S.Yu. Orevkov (2013)
Annales de la faculté des sciences de Toulouse Mathématiques
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For the groups , , , over a finite field we solve the class product problem, i.e., we give a complete list of -tuples of conjugacy classes whose product does not contain the identity matrix.
Robert Guralnick, William M. Kantor, Martin Kassabov, Alexander Lubotzky (2011)
Journal of the European Mathematical Society
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All finite simple groups of Lie type of rank over a field of size , with the possible exception of the Ree groups , have presentations with at most 49 relations and bit-length . Moreover, and have presentations with 3 generators; 7 relations and bit-length , while has a presentation with 6 generators, 25 relations and bit-length .
Piotr Słanina, Witold Tomaszewski (2007)
Bollettino dell'Unione Matematica Italiana
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We use notations: and e . We consider groups generated by , satisfying relations or , . We call groups of the first type mep-groups and of the second type nmep-groups. We show many properties and examples of mep- and nmep-groups. We prove that if is a prime then the group is a nmep-group. We give the necessary and sufficient conditions for metacyclic group to be a nmep-group and we show that nmep-groups with presentation are finite.
Ehud Hrushovski, Anand Pillay (2011)
Journal of the European Mathematical Society
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We study forking, Lascar strong types, Keisler measures and definable groups, under an assumption of NIP (not the independence property), continuing aspects of the paper [16]. Among key results are (i) if does not fork over then the Lascar strong type of over coincides with the compact strong type of over and any global nonforking extension of is Borel definable over , (ii) analogous statements for Keisler measures and definable groups, including the fact that for ...
Alireza Khalili Asboei, Reza Mohammadyari (2016)
Czechoslovak Mathematical Journal
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Let be a finite group, and let be the set of conjugacy class sizes of . By Thompson’s conjecture, if is a finite non-abelian simple group, is a finite group with a trivial center, and , then and are isomorphic. Recently, Chen et al. contributed interestingly to Thompson’s conjecture under a weak condition. They only used the group order and one or two special conjugacy class sizes of simple groups and characterized successfully sporadic simple groups (see Li’s PhD dissertation)....