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The character table of a sharply $5$-transitive subgroup of the alternating group of degree 12 | ||
| International Journal of Group Theory | ||
| مقاله 2، دوره 10، شماره 1، خرداد 2021، صفحه 11-30 اصل مقاله (251.13 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2019.115366.1531 | ||
| نویسندگان | ||
| Nick Gill* ؛ Sam Hughes | ||
| Department of Mathematics, University of South Wales, Treforest, CF37 1DL, U. K. | ||
| چکیده | ||
| We calculate the character table of a sharply $5$-transitive subgroup of Alt(12), and of a sharply $4$-transitive subgroup of Alt(11). Our presentation of these calculations is new because we make no reference to the sporadic simple Mathieu groups, and instead deduce the desired character tables using only the existence of the stated multiply transitive permutation representations. | ||
| کلیدواژهها | ||
| Mathieu groups؛ sporadic groups؛ character table؛ permutation group؛ multiply transitive | ||
| مراجع | ||
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[1] J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, Atlas of finite groups. Maximal subgroups and ordinary characters for simple groups. With comput. assist. from J. G. Thackray., Oxford: Clarendon Press., 1985. [2] G. Frobenius, Uber die Charaktere der mehrfach transitiven Gruppen, ¨ Berl. Ber., 1904 (1904) 558–571.
[3] G. James and M. Liebeck, Representations and characters of groups. 2nd ed, 2nd ed. ed., Cambridge: Cambridge University Press, 2000. [4] F. Ladisch, What did Frobenius prove about M12? (answer), MathOverflow. https://mathoverflow.net/questions/293859/what-did-frobenius-prove-about-m-12/294069#294069.
[5] K. Lux and H. Pahlings, Representations of groups. A computational approach, 124, Cambridge: Cambridge University Press, 2010.
[6] E. Mathieu, Sur la fonction cinq fois transitive de 24 quantit´es, Liouville J. (2), 18 (1873) 25–47.
[7] G. A. Miller, On the supposed five-fold transitive function of 24 elements and 19! ÷ 48 values, Messenger (2) 27 (1897) 187–190. [8] , Sur plusieurs groupes simples., Bull. Soc. Math. Fr., 28 (1900) 266–267.
[9] J. Saxl, The complex characters of the symmetric groups that remain irreducible in subgroups, J. Algebra, 111 (1987) 210–219. [10] G. Frobenius and I. Schur, Uber die reellen Darstellungen der endlichen Gruppen, Berl. Ber. (1906), 186–208. | ||
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