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Papers by Thomas Keller
Proceedings of the Edinburgh Mathematical Society, 2011
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... more 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)geq2smashsqrtp−1k(G)\geq2\smash{\sqrt{p-1}}k(G)geq2smashsqrtp−1 with equality if and only if if smashsqrtp−1\smash{\sqrt{p-1}}smashsqrtp−1 is an integer, G=CprtimessmashCsqrtp−1G=C_{p}\rtimes\smash{C_{\sqrt{p-1}}}G=CprtimessmashCsqrtp−1 and CG(Cp) = Cp. This extends earlier work of Héthelyi, Külshammer, Malle and Keller.
Proceedings of the Edinburgh Mathematical Society, 2011
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... more 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)geq2smashsqrtp−1k(G)\geq2\smash{\sqrt{p-1}}k(G)geq2smashsqrtp−1 with equality if and only if if smashsqrtp−1\smash{\sqrt{p-1}}smashsqrtp−1 is an integer, G=CprtimessmashCsqrtp−1G=C_{p}\rtimes\smash{C_{\sqrt{p-1}}}G=CprtimessmashCsqrtp−1 and CG(Cp) = Cp. This extends earlier work of Héthelyi, Külshammer, Malle and Keller.