Contato

Universidade de Brasília
Campus Universitário Darcy Ribeiro
Departamento de Matemática
Brasília - DF
70910-900, Brasil
mgaronzi at gmail dot com

Martino Garonzi

Research

  I work in Algebra, Group Theory. My currículo lattes. My PhD Thesis.

I mainly work in the field of finite group theory, more specifically:

1. Union coverings. Study of the minimal number of A-orbits of subgroups of a finite group G whose union is G, where A is a subgroup of Aut(G).

2. Factorization with conjugate subgroups. Study of the minimal number of conjugate subgroups (with a given property P) of G whose product is G.

3. Inequalities detecting structural properties of finite groups.

4. Permutation groups, primitive groups.

5. Number of conjugacy classes of a finite group.

6. Number of automorphism orbits of a finite group.

7. Representation theory.

8. Generation of groups.

My publications:

M. Garonzi; Finite Groups that are the union of at most 25 proper subgroups, Journal of Algebra and Its Applications Vol. 12, No. 4 (2013) 1350002.
DOI 10.1142/S0219498810003872
http://www.worldscientific.com/doi/abs/10.1142/S0219498810003872
Arxiv link: http://arxiv.org/abs/1112.5892
 
M. Garonzi, A. Lucchini; Direct products of finite groups as unions of proper subgroups. Arch. Math. (Basel) 95 (2010), no. 3, 201--206.
DOI 10.1007/s00013-010-0155-8
https://link.springer.com/article/10.1007%2Fs00013-010-0155-8
http://arxiv.org/abs/1211.5346
 
M. Garonzi, A. Mar\'oti; Covering certain wreath products with proper subgroups. J. Group Theory 14 (2011), no. 1, 103--125.
DOI 10.1515/jgt.2010.035
https://www.degruyter.com/view/j/jgth.2011.14.issue-1/jgt.2010.035/jgt.2010.035.xml
Arxiv link: http://arxiv.org/abs/1211.5342
 
M. Garonzi; Covering certain monolithic groups with proper subgroups. Communications in algebra, 41:2, 471--491.
DOI 10.1080/00927872.2011.622325
http://www.tandfonline.com/doi/abs/10.1080/00927872.2011.622325}
Arxiv link: http://arxiv.org/abs/1211.5345
 
M. Garonzi; Covering monolithic groups with proper subgroups, Int. J. Group Theory  Vol. 2  No. 1 (2013) 131--144. Per il Proceedings della conferenza Ischia Group Theory 2012.
http://ijgt.ui.ac.ir/?_action=showPDF&article=2674
 
M. Garonzi, D. Levy; Factorizing a Finite Group into Conjugates of a Subgroup,  J. Algebra 418 (2014), 129--141.
DOI 10.1016/j.jalgebra.2014.07.012
http://www.sciencedirect.com/science/article/pii/S0021869314003974
Arxiv link: http://arxiv.org/abs/1407.5937
 
M. Garonzi, A. Lucchini; Covers and normal covers of finite groups. J. Algebra 422 (2015), 148--165.
DOI 10.1016/j.jalgebra.2014.08.046
http://www.sciencedirect.com/science/article/pii/S0021869314005134?via%3Dihub
Arxiv link: http://arxiv.org/abs/1310.1775
 
Garonzi, Martino; Mar\'oti, Attila; On the number of conjugacy classes of a permutation group. J. Combin. Theory Ser. A 133 (2015), 251--260.
DOI 10.1016/j.jcta.2015.02.007
http://www.sciencedirect.com/science/article/pii/S0097316515000266
Arxiv link: http://arxiv.org/abs/1407.5827
 
M. Garonzi; Conjugate factorizations of finite groups. Int. J. Group Theory 4 (2015), no. 2, 69--78. Per il Proceedings della conferenza Ischia Group Theory 2014.
http://ijgt.ui.ac.ir/article_9931.html
 
M. Garonzi, A. Lucchini, Irredundant and minimal covers of finite groups. Comm. Algebra 44 (2016), no. 4, 1722--1727.
DOI 10.1080/00927872.2015.1027383
http://www.tandfonline.com/doi/abs/10.1080/00927872.2015.1027383?journalCode=lagb20
Arxiv link: http://arxiv.org/abs/1412.6275
 
M. Garonzi, Dan Levy, Attila Mar\'oti, Iulian I. Simion; Minimal length factorizations of finite simple groups of Lie type by unipotent Sylow subgroups. J. Group Theory 19 (2016), no. 2, 337--346.
DOI 10.1515/jgth-2015-0051
https://www.degruyter.com/view/j/jgth.2016.19.issue-2/jgth-2015-0051/jgth-2015-0051.xml
 
M. Garonzi, Dan Levy, Attila Mar\'oti, Iulian I. Simion; Factorizations of finite groups by conjugate subgroups which are solvable or nilpotent. Journal of Algebra and Its Applications Vol. 16, No. 1 (2017) 1750043 (19 pages) World Scientific Publishing Company.
DOI 10.1142/S0219498817500438
http://www.worldscientific.com/doi/abs/10.1142/S0219498817500438
Arxiv link: http://arxiv.org/abs/1501.05678
 
M. Garonzi, J. Cannon, D. Levy, A. Mar\'oti, I. I. Simion; Groups equal to a product of three conjugate subgroups. Israel Journal of Mathematics, v. 215, p. 31--52, 2016.
DOI 10.1007/s11856-016-1359-9
https://link.springer.com/article/10.1007%2Fs11856-016-1359-9
Arxiv link: http://arxiv.org/abs/1501.05676
 
M. Garonzi, M. Patassini; Inequalities detecting structural properties of a finite group; Communications in Algebra, v. 45, p. 677--687, 2016.
DOI 10.1080/00927872.2016.1172621
http://www.tandfonline.com/doi/abs/10.1080/00927872.2016.1172621?journalCode=lagb20
Arxiv link: http://arxiv.org/abs/1503.00355
 
M. Garonzi, Dan Levy, Attila Mar\'oti, Iulian I. Simion; Primitive Permutation Groups as Products of Point Stabilizers.  Journal of Algebra (Print), v. 471, p. 399--408, 2017.
DOI 10.1016/j.jalgebra.2016.09.025
http://www.sciencedirect.com/science/article/pii/S0021869316303453
Arxiv link: http://arxiv.org/abs/1508.05659
 
M. Garonzi, A. C. Dantas, R. Bastos; Finite Groups with six or seven automorphism orbits. Journal of Group Theory, v. 1, p. 1, 2017.
DOI 10.1515/jgth-2017-0001
https://www.degruyter.com/view/j/jgth.ahead-of-print/jgth-2017-0001/jgth-2017-0001.xml
Arxiv link: \url{http://arxiv.org/abs/1512.07594}
 
Garonzi, M., Lima, I., On the Number of Cyclic Subgroups of a Finite Group; Bull. Braz. Math. Soc. (N.S.) 49 (2018), no. 3, 515–530. https://doi.org/10.1007/s00574-018-0068-x
DOI 10.1007/s00574-018-0068-x
https://link.springer.com/article/10.1007/s00574-018-0068-x
Arxiv link: https://arxiv.org/abs/1707.07293v2
 
Garonzi, M., Lucena Dias, M., Group Partitions of Minimal Size; Journal of Algebra (2019), DOI https://doi.org/10.1016/j.jalgebra.2019.04.017
DOI 10.1016/j.jalgebra.2019.04.017
https://doi.org/10.1016/j.jalgebra.2019.04.017
Arxiv link: https://arxiv.org/abs/1811.02996
 
Garonzi, M., Lucchini, A., Maximal irredundant families of minimal size in the alternating group. Arch. Math. (2019). https://doi.org/10.1007/s00013-019-01331-8
DOI 10.1007/s00013-019-01331-8
http://dx.doi.org/10.1007/s00013-019-01331-8
Arxiv link: https://arxiv.org/abs/1808.04387