Brauer trees for blocks of cyclic defect in the groups \(G_ 2(q)\) for primes dividing \(q^ 2\pm q+1\)
Let \(G_ 2(q)\) be the finite Chevalley group of type \(G_ 2\) over the field with q elements (q a prime power not divisible by 2 and 3) of order \(q^ 6(q+1)^ 2(q-1)^ 2(q^ 2+q+1)(q^ 2-q+1)\). In this paper the author gives the distribution of the ordinary irreducible characters of \(G_ 2(q)\) into the p-blocks for the primes \(p\neq 2,3\) dividing \(q^ 2\pm q+1\). Furthermore the decomposition matrices of the p-blocks of cyclic defect are determined and described in form of their Brauer trees.
scientific article; zbMATH DE number 4103327