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Lucchini, Andrea. (1396). Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements. سامانه مدیریت نشریات علمی دانشگاه اصفهان, 7(1), 17-21. doi: 10.22108/ijgt.2017.21220
Andrea Lucchini. "Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements". سامانه مدیریت نشریات علمی دانشگاه اصفهان, 7, 1, 1396, 17-21. doi: 10.22108/ijgt.2017.21220
Lucchini, Andrea. (1396). 'Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements', سامانه مدیریت نشریات علمی دانشگاه اصفهان, 7(1), pp. 17-21. doi: 10.22108/ijgt.2017.21220
Lucchini, Andrea. Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements. سامانه مدیریت نشریات علمی دانشگاه اصفهان, 1396; 7(1): 17-21. doi: 10.22108/ijgt.2017.21220

Detecting the prime divisors of the character degrees and the class sizes by a subgroup generated with few elements

International Journal of Group Theory
مقاله 4، دوره 7، شماره 1، خرداد 2018، صفحه 17-21    اصل مقاله (183.48 K)
نوع مقاله: Ischia Group Theory 2016
شناسه دیجیتال (DOI): 10.22108/ijgt.2017.21220
نویسنده
Andrea Lucchini*
Dipartimento di Matematica Università di Padova
چکیده
We prove that every finite group $G$ contains a three-generated subgroup $H$ with the following property‎: ‎a prime $p$ divides the degree of an irreducible character of $G$ if and only if it divides the degree of an irreducible character of $H.$ There is no analogous result for the prime divisors of the sizes of the conjugacy classes‎.
کلیدواژه‌ها
‎Character degrees؛ class sizes
مراجع
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[7] A. Lucchini and F. Menegazzo, Generators for finite groups with a unique minimal normal subgroup, Rend. Sem. Mat. Univ. Padova, 98 (1997) 173-191.

[8] A. Lucchini, M. Morigi and P. Shumyatsky, Boundedly generated subgroups of finite groups, Forum Math., 24 no. 4 (2012) 875–887.

[9] G. O. Michler, Brauers conjectures and the classification of finite simple groups, Lecture Notes in Math, 1178, Springer, Berlin, 1986 129–142.

[10] J. S. Williams, Prime graph components of finite groups, J. Algebra, 69 (1981) 487–513.

[11] A. V. Zavarnitsine, On the recognition of finite groups by the prime graph, Algebra and Logic, 45 (2006) 220–231.

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