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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S. V. Jablan (1986)
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...
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...
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....
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...
Gaurav Mittal, Rajendra Kumar Sharma (2021)
Mathematica Bohemica
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We characterize the unit group of semisimple group algebras of some non-metabelian groups, where is a field with elements for prime and a positive integer . In particular, we consider all 6 non-metabelian groups of order 48, the only non-metabelian group of order 54, and 7 non-metabelian groups of order 72. This completes the study of unit groups of semisimple group algebras for groups upto order 72.
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). ...
Behnam Ebrahimzadeh, Reza Mohammadyari (2019)
Archivum Mathematicum
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One of the important questions that remains after the classification of the finite simple groups is how to recognize a simple group via specific properties. For example, authors have been able to use graphs associated to element orders and to number of elements with specific orders to determine simple groups up to isomorphism. In this paper, we prove that Suzuki groups , where is a prime number can be uniquely determined by the order of group and the number of elements with the same...
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.
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...
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.
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...
Wenyang Wang, Ni Du (2021)
Czechoslovak Mathematical Journal
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Let be a finite group. If has two rows which differ in only one entry in the character table, we call an RD1-group. We investigate the character tables of RD1-groups and get some necessary and sufficient conditions about RD1-groups.
Zeinab Araghi Rostami, Mohsen Parvizi, Peyman Niroomand (2024)
Czechoslovak Mathematical Journal
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We conduct an in-depth investigation into the structure of the Bogomolov multiplier for groups of order and exponent . We present a comprehensive classification of these groups, identifying those with nontrivial Bogomolov multipliers and distinguishing them from groups with trivial multipliers. Our analysis not only clarifies the conditions under which the Bogomolov multiplier is nontrivial but also refines existing computational methods, enhancing the process of...
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 .
Federico Menegazzo, Martin L. Newell (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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Fitting classes and injectors are discussed in the class of -groups. A necessary and sufficient condition for the existence of injectors is given; it is also shown that, when this condition holds, the injectors form a unique conjugacy class.