Counting lifts of Brauer characters

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In this paper we examine the behavior of lifts of Brauer characters in p-solvable groups where p is an odd prime. In the main result, we show that if ϕ∈ IBrp(G) is a Brauer character of a solvable group such that ϕhas an abelian vertex subgroup Q, then the number of lifts of ϕin Irr(G) is at most |Q|. In order to accomplish this, we develop several results about lifts of Brauer characters in p-solvable groups that were previously only known to be true in the case of groups of odd order.