Groups and their representations  Page description

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Details of project

  
Identifier
38059
Type K
Principal investigator Pálfy, Péter Pál
Title in Hungarian Csoportok és reprezentációik
Title in English Groups and their representations
Panel Mathematics and Computing Science
Department or equivalent Department of Algebra and Number Theory (Eötvös Loránd University)
Participants Abért, Miklós
Bódi, Viktor
Corrádi, Keresztély
Csörgo, Piroska
Hermann, Péter
Pelikán, József
Podoski, Károly
Pyber, László
Szabó, Csaba
Szegedy, Balázs
Starting date 2002-01-01
Closing date 2006-12-31
Funding (in million HUF) 11.581
FTE (full time equivalent) 0.00
state closed project





 

Final report

  
Results in Hungarian
Változatos kérdéseket vizsgáltunk a csoportelméletben, a csoportok reprezentációelméletében és más kapcsolódó absztrakt algebrai területeken. 39 tudományos dolgozatot publikáltunk, ezek nagy részét vezető nemzetközi folyóiratokban (pl. Bulletin of the London Mathematical Society, Duke Mathematical Journal, European Journal of Combinatorics, Journal of Algebra, Journal of Group Theory, Proceedings of the American Mathematical Society). Legfontosabb eredményeink a következők: Meghatároztuk a pozitiv karakterisztikájú globális testek feletti aritmetikai csoportok kongruenciarészcsoport-növekedését. Új példákat találtunk olyan csoportokra, amelyeknek izomorf a pro-véges lezárásuk. Teljes leirását adtuk azoknak a moduláris csoportalgebráknak, melyek Lie nilpotencia-indexe maximális. Csoportelméleti módszereket alkalmazva a loopok elméletében olyan (128 elemű) loopot konstruáltunk, amelynél a belső permutációk csoportja kommutativ és a loop nilpotnecia osztálya 3, ezzel Bruck egy 60 éves kérdésére adtunk választ. Az univerzális algebrában a véges moduláris hálók egy széles osztályára konstruáltunk véges kongruencia-reprezentációkat, mégpedig operátorcsoportok felhasználásával. A bonyolultságelméletben több algebrai problémát tanulmányoztunk. Például megmutattuk, hogy nem feloldható csoportokban az azonosságok ellenőrzése NP-teljes probléma.
Results in English
We studied various questions in group theory, in representation theory of groups, and in related areas of abstract algebra. We published 39 research papers, many of them in leading international journals (for example, Bulletin of the London Mathematical Society, Duke Mathematical Journal, European Journal of Combinatorics, Journal of Algebra, Journal of Group Theory, Proceedings of the American Mathematical Society). The most important results are the following: We determined the congruence subgroup growth of arithmetic groups over global fields of positive characteristic. We found new examples of groups with isomorphic pro-finite closure. We gave a complete description of modular group algebras with maximal Lie nilpotency index. Applying group theoretic methods in loop theory, we constructed an example of a loop (of order 128) with an Abelian inner permutation group and of nilpotency class 3, thereby answering a 60-year old question of Bruck. In universal algebra we constructed finite congruence lattice representations for a large class of finite modular lattices, namely by using operator groups. In complexity theory we studied several algebraic problems. For example, we showed that for nonsolvable groups the checking of identities is an NP-complete problem.
Full text http://real.mtak.hu/463/
Decision
Yes





 

List of publications

  
M. Abért, N. Nikolov, B. Szegedy: Congruence subgroup growth of arithmetic groups in positive characteristic, Duke Math. J. 117, 367-383, 2005
P. Csörgő, A. Drapal: Left conjugacz closed loops of nilpotencz class two, Resultate der Math. 47, 242-265, 2005
M. Asaad, A. A. Heliel, M. Ezzat Mohamed, P. Csörgő: Finite groups with some subgroups permutable with all Sylow subgroups, JPANTA 4, 437-446, 2004
M. Asaad, P. Csörgő: Characterization of finite groups with some S-quasinormal subgroups, Monatshefte fur Mathematik 146, 263-266, 2005
V. Bovdi, E. Spinelli: Modular group algebras with maximal Lie nilpotency indices, Publ. Math. Debrecen, 65, 243-252, 2004
V. Bovdi, C. Höfert, W. Kimmerle: On the first Zassenhaus conjecture for integral group rings, Publ. Math. Debrecen 65, 291-303, 2004
V. Bovdi, P. Gudivok, V. Rudko: Torsion free groups with indecomposable holonomy group II, J. Group Theory 7, 555-569, 2004
P. Csörgő, M. Herzog: On supersolvable groups and the nilpotator, Comm. Algebra 32, 609-620, 2004
P. Csörgő, T. Kepka: On loops whose inner permutations commute, Comment. Math. Univ. Carolinae 45, 213-221, 2004
P. Csörgő: Extending the structural homomorphism of LCC loops, Comment Math. Univ. Carolinae 46, 385-389, 2005
P. Hegedűs, P. P. Pálfy: Finite modular congruence lattices, Algebra Universalis 54, 105-120, 2005
P. Csörgő, A. Jancarik, T. Kepka: Generalized capable abelian groups, Non-associative algebra and its applications, LNPAM vol.246, 129-136, 2005
S. Seif, Cs. Szabó: Algebra complexity problems involving graph homomorphism, semigroups and the constraint satisfaction problem, J. Complexity 19, 153-160, 2003
B. Szegedy: Characters of Borel and Sylow subgroups of classical groups, J. Algebra 267, 130-136, 2003
Cs. Szabó, S. Seif: Computational complexity of checking identities in 0-simple semigroups and matrix semigroups over finite fields, Semigroup Forum 72, 207-222, 2006
Cs. Szabó, V. Vértesi: The complexity of the word-problem for finite matrix rings, Proc. Amer. Math. Soc. 132, 3689-3695, 2004
P. P. Pálfy: Maximal clones and maximal permutation groups, Közlésre elfogadva, Discuss. Math., 2006
P. P. Pálfy: A non-power-hereditarz congruence lattice representation of M3, Közlésre elfogadva, Publ. Math. Debrecen, 2006
K. Podoski, B. Szegedy: Bounds for the index of the centre in capable groups, Proc. Amer. Math. Soc. 133, 3441-3445, 2005
M. Abért: Group laws and free subgroups in topological groups, Bull.London Math. Soc. 37, 525-534, 2005
P. Csörgő: Abelian inner mapping group and nilpotency class greater than two, Közlésre elfogadva, European J. Combinatorics, 2006
Cs. Szabó: On rings with few orbits, Commun. Algebra 34, 2251-2260, 2006
P. Csörgő: On connected transversals to abelian subgroups and loop theoretical consequences, Arch. Math. 86, 499-516, 2006
Cs. Szabó, G. Kun: Jónsson terms and near-unanimity functions in finite posets, Order 20, 291-298, 2004
E. Szabó: Formations of absolutely solvable groups, Közlésre elfogadva, Publ. Math. Debrecen, 2006
E. Szabó: Embedding into absolutely solvable groups, Közlésre elfogadva, Publ. Math. Debrecen, 2006
P. P. Pálfy, O. Steinfeld: Some group theoretic problems inspired by ring theoretic analogies, Math. Pannon. 13, 167-174, 2006
Z. Halasi: On the characters of the unit group of DN-algebras, J. Algebra 302, 678-685, 2006
V. Bovdi, T. Juhász, E. Spinelli: Modular group algebras with almost maximal Lie nilpotency indices, I, Algebras and Representation Theory 9, 1-10, 2006
V. Bovdi: Modular group algebras with almost maximal Lie nilpotency indices, II, Közlésre elfogadva, Sci. Math. Japon., 2006
V. Bovdi: On a filtered multiplicative basis of group algebras, II, Algebras and Representation Theory 6, 353-368, 2003
V. Bovdi, V. Rudko: Extensions of the representation modules of a prime order group, J. Algebra 295, 441-451, 2006
V. Bovdi: Symmetric units and group identities in group algebra I, Acta Math. Acad. Paedagog. Nyházi. 22, 149-159, 2006
L. Pyber: Old groups can learn new tricks, Groups, combinatorics and geometry, 243-255, 2003
Cs. Szabó, G. Horváth, J. Lawrence, L. Mérai: The complexity of the equivalence problem for nonsolvable groups, Közlésre elfogadva, Bull. London Math. Soc., 2006
Cs. Szabó, K. Kátai: The free spectrum of the variety generated by the 5-element Brandt semigroup, Közlésre elfogadva, Semigroup Forum, 2006
Cs. Szabó, G. Horváth: The complexity of checking identities over finite groups, Közlésre elfogadva, Int. J. Algebra and Comp., 2006
Cs. Szabó, V. Vértesi: The complexity of checking identities for finite matrix rings, Algebra Universalis 51, 439-445, 2004
M. Abért, B. Virág: Dimension and randomness in groups acting on rooted trees, J. Amer. Math. Soc. 18, 157ü192, 2005



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