Abstract
In this paper, we determine new characterizations of nested and nested GVZ-groups, including character-free characterizations, but we additionally show that nested groups and nested GVZ-groups can be defined in terms of the existence of certain normal series.
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Berkovich, Y.: Groups of Prime Power Order. De Gruyter Expositions in Mathematics, vol. 1. Walter de Gruyter GmbH & Co. KG, Berlin (2008)
Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system I: the user language. J. Symb. Comput. 24, 235–265 (1997)
Burkett, S.T., Lewis, M.L.: Characterizations of nested GVZ-groups by central series. arXiv:1907.04795
Burkett, S.T., Lewis, M.L.: GVZ-groups. arXiv:1909.05841. Submitted for publication
Burkett, S.T., Lewis, M.L.: A characterization of nested groups in terms of conjugacy classes. Comptes rendus Mathematique. arXiv:1909.05849. Submitted for publication
Camina, A.R.: Some conditions which almost characterize Frobenius groups. Isr. J. Math. 31, 153–160 (1978)
Erné, M., Koslowski, J., Melton, A., Strecker, G.E.: A primer on Galois connections in Papers on general topology and applications. Ann. N.Y. Acad. Sci. 1993, 103–125 (1991)
Fernández-Alcober, G.A., Moretó, A.: Groups with two extreme character degrees and their normal subgroups. Trans. Am. Math. Soc. 353, 2171–2192 (2001)
Isaacs, I.M.: Character Theory of Finite Groups. Dover Publications Inc, New York (1994)
Isaacs, I.M.: Subgroups generated by small classes in finite groups. Proc. Am. Math. Soc. 136, 2299–2301 (2008)
Lewis, M.L.: Character Tables of Groups Where All Nonlinear Irreducible Characters Vanish Off the Center, Ischia Group Theory 2008, pp. 174–182. World Sci. Publ, Hackensack, NJ (2009)
Lewis, M.L.: The vanishing-off subgroup. J. Algebra 321, 1313–1325 (2009)
Lewis, M.L.: Groups where the centers of the irreducible characters form a chain. Monatshefte für Mathematik. arXiv:1902.10689. Submitted for publication
Longobardi, P., Maj, M., Mann, A.: Minimal classes and maximal class in \(p\)-groups. Isr. J. Math. 110, 93–102 (1999)
Mann, A.: Elements of minimal breadth in finite p-groups and Lie algebras. J. Aust. Math. Soc. 81, 209–214 (2006)
Mann, A.: Conjugacy class sizes in finite groups. J. Aust. Math. Soc. 85, 251–255 (2008)
Mattarei, S.: Retrieving information about a group from its character table. Ph.D. dissertation University of Warwick (1992)
Mlaiki, N.M.: Camina triples. Can. Math. Bull. 57, 125–131 (2014)
Nenciu, A.: Isomorphic character tables of nested GVZ-groups. J. Algebra Appl. 11, 12 (2012)
Nenciu, A.: Nested GVZ-groups. J. Group Theory 19, 693–704 (2016)
Verardi, L.: Gruppi semiextraseciali di esponente \(p\). Ann. Mat. Pura Appl. (4) 148, 131–171 (1987)
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Communicated by John S. Wilson.
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Burkett, S.T., Lewis, M.L. Groups where the centers of the irreducible characters form a chain II. Monatsh Math 192, 783–812 (2020). https://doi.org/10.1007/s00605-019-01362-x
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DOI: https://doi.org/10.1007/s00605-019-01362-x