On a question of Bumagin and Wise

Alan Logan

Wednesday 28th October, 2015 16:00-17:00 Maths 522


Bumagin and Wise asked if every countable group Q can be realised as the outer automorphism group of a finitely generated, residually finite group G_Q. We further assume that Q is finitely generated. We give a partial solution when G_Q is recursively presentable, and a complete solution in this case modulo an open question of Osin. We give the first examples of groups G_Q where Q is not recursively presentable.

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