Character Theory of Finite Groups

By M. Lewis, Gabriel Navarro, D. Passman, T. Wolf. 2010

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Brauer's Height Zero Conjecture (2022, neutral): “By Gallagher’s Corollary 6.17 of [26], we have δ = ˜ νβ , for some β ∈ Irr( D/L ).”
Word maps, conjugacy classes, and a noncommutative Waring-type theorem (2009, methodology): “By the generalized orthogonality relations (see Isaacs [14]) we haveX 2IrrG j .xi /j 2 D jCG.xi /j: In particular j .x1/j jCG.x1/j1=2 for all .”
Intersecting Families of Permutations (2010, background): “For more background, the reader may consult [18] and [28].”
Spectra of Graphs (2011, positive): “We follow Isaacs [247], who follows Brauer.”
A Machine-Checked Proof of the Odd Order Theorem (2013, background): “Examples of finite groups include the cyclic group Z/nZ of integers modulo n under addition, with identity 0; the set Sn of permutations of {0, . . . , n − 1}, under composition; and the set of isometries of a regular n-sided polygon.”
A reduction theorem for the Alperin–McKay conjecture (2012, methodology): “8 (c) requires some further preparation: we associate to y A Irrp 0 ðKÞ and y 0 :1⁄4 ŴðyÞ projective representations of Xy and NX ðM̂Þy 0 satisfying the three equations of [17], Theorem 11.”