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In this article, we study the elements with disconnected centralizer in the Brauer complex associated to a simple algebraic group defined over a finite field with corresponding Frobenius map and derive the number of -stable semisimple classes of with disconnected centralizer when the order of the fundamental group has prime order. We also discuss extendibility of semisimple characters of the fixed point subgroup to their inertia group in the full automorphism group. As a consequence, we...
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