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A lower bound of the Perron-Frobenius eigenvalue of the Cartan matrix of a finite group (1999)

Wada, T.

Springer

Archiv der Mathematik 73 (1999), S. 407-413

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ISSN: 1420-8938

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract. In this article we exhibit a relation between the number k(B) of ordinary irreducible characters in a p-block B of a finite group G and the Cartan invariants c ij of B. Next, we give a lower bound of the Perron-Frobenius eigenvalue $\rho (C_B)$ of the Cartan matrix C B of B in terms of B, that is $k(B) \le \rho (C_B)l(B)$ , where l(B) is the number of irreducible Brauer characters in B. For p-solvable groups, we conjecture $k(B) \le \rho (C_B)$ that is closely related to the Brauer's k(B) conjecture.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s000130050416

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