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Details of project

  
Identifier
49841
Type K
Principal investigator Corrádi, Keresztély
Title in Hungarian Csoportelmélet
Title in English Group Theory
Panel Mathematics and Computing Science
Department or equivalent Department of Software Techology and Methodology (Eötvös Loránd University)
Participants Csörgo, Piroska
Elek, Gábor
Hermann, Péter
Héthelyi, László
Horváth, Erzsébet
Pálfy, Péter Pál
Pyber, László
Szegedy, Balázs
Starting date 2005-01-01
Closing date 2009-12-31
Funding (in million HUF) 15.790
FTE (full time equivalent) 18.25
state closed project





 

Final report

  
Results in Hungarian
Kutatások az alábbi területeken: Végtelen csoportokon belül: Aszimptotikus csoportelmélet A Tavgen-sejtés (ha G reziduálisan véges BG-csoport, akkor lineáris) igazolása, ha 1) G majdnem végtelen, azaz nincs végtelen indexű normálosztója, vagy 2) G reziduálisan véges-feloldható. Egy n-elemű csoportnak legfeljebb cn^1.5 darab maximális részcsoportja lehet. Topológikus csoportok és gráfok Véges csoportokon belül: Tiszta csoportelmélet Csoportok és loop-ok Véges csoportok közönséges és moduláris reprezentációelmélete
Results in English
Investigations in the following areas: Concerning infinite groups: Asymptotic group theory Proof of Tavgen's conjecture (all residually finite BG-groups are linear) provided 1) G is just infinite (has no normal subgroup of infinite index), or 2) G is residually finite-solvable The number of maximal subgroups in a group of order n is at most cn^1.5 Topological groups and graphs Concerning finite groups: Pure group theory Groups and loops Ordinary and modular representation theory of finite groups
Full text https://www.otka-palyazat.hu/download.php?type=zarobeszamolo&projektid=49841
Decision
Yes





 

List of publications

  
Corrádi K., Szabó S.: Rédei's theorem is a consequence of its (p,p) special case and Hajós' theorem, Mediterr. J. Math. 4 (1) (2007), 109 - 117., 2007
Corrádi K., Szabó S.: Factoring Abelian groups into uniquely complemented subsets, közlésre leadva, 2011
P. Hegedűs, P. P. Pálfy: Finite modular congruence lattices, Algebra Universalis 54 pp. 105-120., 2005
Maróti A.: Symmetric functions, generalized blocks, and permutations with restricted cycle structure, European Journal of Combinatorics 28 (2007), no. 3, 942–963., 2007
Maróti A.: On generalized blocks for alternating groups, Journal of Algebra 297 (2006), no. 2, 400-408., 2006
Héthelyi L.-Horváth E.-B. Külshammer-J. Murray: Central Ideals and Cartan Invariants of Symmetric Algebras, J. ALgebra (293) pp. 243-260., 2005
Th. Breuer, Héthelyi L., Horváth E., B. Külshammer, J. Murray: Cartan Invariants and Central Ideals of Group Algebras, J. Algebra 296 (2006), 177-195., 2006
Corrádi K., Héthelyi L., Horváth E.: On one-sided stabilizers of subsets of finite groups, Arch. Math. 86 (2006) 295-304., 2006
Héthelyi L.-B. Külshammer: Elements of prime power order and their conjugacy classes in finite groups, J. of Australian Math. Soc. (78), pp. 1-5., 2005
Corrádi K., Hermann P., Héthelyi L., Horváth E.: Miscellaneous results on supersolvable groups, Proceedings of Groups St Andrews 2009 in Bath (közlésre elfogadva), 2010
Csörgő P.: Extending the structural homomorphism of LCC loops, Comment. Math. Univ. Carolinea 46,3 pp. 385-389., 2005
Csörgő P., A. Drapal: Left conjugacy closed loops of nilpotency class two, Result. Math. 47 pp. 242-265., 2005
Csörgő P.: Abelian inner mapping group and nilpotency class greater than two, European Journal of Combinatorics 28 (2007), 858-867, 2007
Csörgő P.: On connected transversals to abelian subgroups and loop theoretical consequences, Arch. Math. 86 (2006), 499-516., 2006
D. Segal, Pyber L: Finitely generated groups with polynomial index growth, közlésre elfogadva: J. reine u. angew. Math., 2009
Elek G., T. Ceccherini: Minimal topological actions do not determine the measurable orbit equivalence class, közlésre leadva, 2009
Elek G.: The Strong Approximation Conjecture holds for amenable groups, Journal of Functional Analysis, 2006 Volume 239 (1), pp. 345-355., 2006
Elek G.: Weak convergence of finite graphs, integrated density of states and a Cheeger inequality, Journal of Combinatorial Theory (B), közlésre elfogadva, 2009
Elek G.: The combinatorial cost, l'Enseignement Math. (53) 225-236., 2007
Elek G.: L2-spectral invariants and quasi-cristal graphs, közlésre leadva, 2009
Elek G.: Aperiodic order, integrated density of states and the continuous algebras of John von Neumann., közlésre leadva, 2009
M. W. Liebeck , Pyber L., A. Shalev: On a conjecture of G. E. Wall, J. Algebra 317 (2007) 184 –197, 2007
Maróti A., John R. Britnell, Anton Evseev, Robert M. Guralnick, Petra E. Holmes: Sets of elements that pairwise generate a linear group, Journal of Combinatorial Theory Ser. A. 115 (2008), no. 3, 442–465., 2008
Maróti A.: A proof of a generalized Nakayama conjecture, Bulletin of the London Mathematical Society 35 (2006), no. 5, 777-785., 2006
Maróti A., Petra E. Holmes: Pairwise generating and covering sporadic simple groups, Journal of Algebra (Section on Computational Algebra) (közlésre elfogadva), 2010
G. Bacsó, L. Héthelyi and P. Sziklai: New near-factorizations of finite groups, Studia Sci. Math. Hungar. 45 (4) (2008), 493-510., 2008
P. Csörgő, A. Jancarik, T. Kepka: Generalized capable abelian groups, Non-Associativ Algebra and its Applications, A series of Lecture Notes in Pure and Applied Mathematics, Vol. 246, Chapt.10, p. 129-136 (2006), 2006
M. Asaad, P. Csörgő, M. Ramadan: Normal pi-complements for finite groups, Acta Math. Hung. 119 (2008), 359-364., 2008
M. Asaad, P. Csörgő: Some results on supersolvability of finite groups, Monatsh. Math. 154 (2008), 265-269., 2008
P. Csörgő, A. Drapal,: On left conjugacy closed loops in which the left multiplication group is normal, Abh. Math. Sem. Univ. Hamburg 76 (2006) 17-34., 2007
Elek G.: L2-spectral invariants and convergent sequences of finite graphs, Journal of Functional Analysis, 254 (2008) 2667-2689., 2008
Maróti A., Bereczky Á.: On groups with all normal subgroups transitive or semiregular, Journal of Algebra 319 (2008), no. 4, 1733–1751., 2008
J. Kempe, L. Pyber, A. Shalev: Permutation groups, minimal degrees and quantum computing, Groups, Geometry and Dynamics, közlésre elfogadva, 2009
Héthelyi L., Horváth E.: Galois actions on blocks and classes of finite groups, J. Algebra 320 (2008), 660-679., 2008
Csörgő P., A. Drapal: On loops rich in automorphisms that are abelian modulo the nucleus, Forum Mathematicum 21/3 (2009), 477-489., 2009
Csörgő P.: On loops that are abelian over the nucleus and Buchsteiner loops with commuting inner mappings, Comment. Math.Univ. Carolin. 49 2 (2008) 197-208., 2008
Csörgő P., A. Drapal, M. K. Kinyon: Buchsteiner loops, International Journal of Algebra and Computation (közlésre elfogadva), 2010
Csörgő P., A. Drapal: Buchsteiner loops and conjugacy closedness, Comm. in Algebra -- közlésre elfogadva, 2010
Pálfy P. P.: Some functionally complete minimal clones, Acta Sci. Math. (Szeged) 73 (2007), 963-971, 2007
Elek G., Lippner G.: A bounded degree analogue of the Szemeredi Regularity Lemma for bounded degree graphs., közlésre benyújtva, 2009
Maróti A., A. Lucchini, D. Semmen: d-wise generation of some infinite groups, Journal of Algebra and Its Applications Vol. 7. Issue 6. (2008). 717-723., 2008
Maróti A., A. Lucchini: Some results and questions related to the generating graph of a finite group, Proceedings of the Ischia Group Theory Conference 2008., 2009
Maróti A., A. Lucchini: On finite simple groups and Kneser graphs, Journal of Algebraic Combinatorics. Vol. 30. Number 4. (2009) 549-566., 2009
Maróti A., A. Lucchini: On the clique number of the generating graph of a finite group, Proceedings of the American Mathematical Society. Vol. 137 (2009) 3207--3217., 2009
Héthelyi L., D. J. Green, L. M. Lilienthal: On Oliver's p-group conjecture, J. Algebra and Number Theory -- közlésre elfogadva, 2009
D. J. Green, L. Héthelyi, N. Mazza: On Oliver's p-group conjecture II., Mathematische Annalen (közlésre elfogadva), 2010
L. Héthelyi, B. Külshammer: Conjugacy classes and characters of finite p-groups, Communications in Algebra (közlésre elfogadva), 2010
L. Héthelyi, E. Horváth, T. M. Keller, A. Maróti: Groups with few conjugacy classes, közlésre leadva, 2011
Maróti A., A. Lucchini: Rings as the unions of proper subrings, közlésre leadva, 2011
Maróti A., M. Garonzi: Covering certain wreath products with proper subgroups, közlésre leadva, 2011
Maróti A., Th. Breuer, R. M. Guralnick, A. Lucchini, G. P. Nagy: Hamiltonian cycles in the generating graphs of finite groups, közlésre leadva, 2011
Maróti A., Ch. Lanski: Ring elements as sums of units, Central European Journal of Mathematics. Vol. 7. Number 3. (2009) 395--399., 2009
M.Asaad, Csörgő P.: Some results on supersolvability of finite groups, közlésre leadva, 2011



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