ON AN INERTIA FACTOR GROUP OF 2\(^{8}\):\(O_8^{+}\)(2) - Moori, Jamshid; Seretlo, Thekiso (Italian Journal of Pure and Applied Mathematics, 2014)
ON AN INERTIA FACTOR GROUP OF 2\(^{8}\):\(O_n ^{+}\)(2) The group \(\bar{G}\) = 26:A8 is an inertia factor group of 2\(^{8}\):\(O_8^{+}\)(2). As an inertia factor group, our group \(\bar{G}\) plays an essential role in the construction of the character table of 2\(^{8}\):\(O_n ^{+}\)(2). In this paper we look at two ways of constructing \(\bar{G}\). In the first method, we use combinatorics and the natural action of A8 on W \(\cong\) 26. In the second method, we use a computational method to construct \(\bar{G}\) = N:A8 inside \(O_8^{+}\)(2). We show that A8 acts irreducibly on both W and N and we prove that the two groups are indeed isomorphic.