One namesake of this result is also the namesake of an order formula for objects containing only two conjugacy classes, and that namesake also names a series with McKay used to prove the "moonshine conjecture" of Conway and Norton. Bender's method wa
One namesake of this result is also the namesake of an order formula for objects containing only two conjugacy classes, and that namesake also names a series with McKay used to prove the "moonshine conjecture" of Conway and Norton. Bender's method was used to streamline the proof of this result. This result was first proven based on work done by Michio Suzuki, and was restricted to objects for which the centralizer of every non-trivial element is nilpotent. The proof of this result showed that each non-trivial irreducible character arises only once as an exceptional character, and used the method of local analysis; that proof was over 200 pages long. This theorem was originally developed based on a conjecture by Burnside, which asked whether finite simple groups of odd order exist. For 10 points, name this seminal result in group theory, which states that every finite group of odd order is solvable.
One namesake of this result is also the namesake of an order formula for objects containing only two conjugacy classes, and that namesake also names a series with McKay used to prove the "moonshine conjecture" of Conway and Norton.