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Creators/Authors contains: "NAVARRO, GABRIEL"

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  1. Abstract We prove that the number of conjugacy classes of a finite groupGconsisting of elements of odd order, is larger than or equal to that number for the normaliser of a Sylow 2-subgroup ofG. This is predicted by the Alperin Weight Conjecture. 
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  2. Abstract IfGis a finite group, we have proposed three new conjectures on the interaction between different primes and their corresponding Brauer principal blocks. In this paper,we give strong support to the validity of Conjectures B and C. 
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  3. Abstract Let be a finite group and and be different primes. Assume that is odd and . We prove that if divides the degrees of the nonlinear irreducible ‐modular representations, then has a normal ‐complement. 
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  4. Abstract We study the fields of values of the irreducible characters of a finite group of degree not divisible by a prime p . In the case where $p=2$ , we fully characterise these fields. In order to accomplish this, we generalise the main result of [ILNT] to higher irrationalities. We do the same for odd primes, except that in this case the analogous results hold modulo a simple-to-state conjecture on the character values of quasi-simple groups. 
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