Quasi-semisimple profinite groups have polynomial representation growth precisely when their semisimple parts do, with equal growth degrees under bounded Lie rank, and constructions exist for any positive real growth degree with flexible composition factors.
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Representation growth of quasi-semisimple profinite groups
Quasi-semisimple profinite groups have polynomial representation growth precisely when their semisimple parts do, with equal growth degrees under bounded Lie rank, and constructions exist for any positive real growth degree with flexible composition factors.