论文信息 - Groups with few conjugacy classes

Groups with few conjugacy classes

Abstract Let G be a finite group, let p be a prime divisor of the order of G and let k(G) be the number of conjugacy classes of G. By disregarding at most finitely many non-solvable p-solvable groups G, we have $k(G)\geq2\smash{\sqrt{p-1}}$ with equality if and only if if $\smash{\sqrt{p-1}}$ is an integer, $G=C_{p}\rtimes\smash{C_{\sqrt{p-1}}}$ and CG(Cp) = Cp. This extends earlier work of Héthelyi, Külshammer, Malle and Keller.

T. Keller | A. Maróti | E. Horváth | L. Héthelyi

[1] T. Keller. Lower bounds for the number of conjugacy classes of finite groups , 2007, Mathematical Proceedings of the Cambridge Philosophical Society.

[2] G. Malle. Fast-einfache Gruppen mit langen Bahnen in absolut irreduzibler Operation , 2006 .

[3] B. Külshammer,et al. On The Number of Conjugacy Classes of a Finite Solvable Group , 2000 .

[4] T. Wolf,et al. Representations of Solvable Groups , 1993 .

[5] L. Pyber,et al. Finite Groups Have Many Conjugacy Classes , 1992 .

[6] Martin W. Liebeck,et al. The Subgroup Structure of the Finite Classical Groups , 1990 .

[7] Suzanne M. Seager. The rank of a finite primitive solvable permutation group , 1987 .

[8] E. Landau. Über die Klassenzahl der binären quadratischen Formen von negativer Discriminante , 1903 .

[9] J. Pintz,et al. Landau’s problems on primes , 2009 .

[10] Meinolf Geck,et al. Group representation theory , 2007 .

[11] Olaf Manz,et al. Representations of Solvable Groups: Contents , 1993 .

[12] J. Conway,et al. Atlas of finite groups : maximal subgroups and ordinary characters for simple groups , 1987 .

[13] Juan Antonio Vera López,et al. Classification of finite groups according to the number of conjugacy classes II , 1986 .

[14] Meinolf Geck,et al. Finite groups of Lie type , 1985 .

[15] Antonio Vera López,et al. Classification of finite groups according to the number of conjugacy classes , 1985 .