University of Cambridge > Talks.cam > Algebra and Representation Theory Seminar > On the residual finiteness of outer automorphism groups

On the residual finiteness of outer automorphism groups

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  • UserAshot Minasyan (Southampton)
  • ClockWednesday 16 February 2011, 16:30-17:30
  • HouseMR15.

If you have a question about this talk, please contact Christopher Brookes.

A group G is said to be residually finite if the intersection of all finite index subgroups is trivial in G. In 1963 G. Baumslag proved that the full automorphism group Aut(G), of a finitely generated residually finite group G, is residually finite. In general, this result cannot be extended to the outer automorphism group Out(G)=Aut(G)/InnG. In fact, Bumagina and Wise showed that for any finitely presented group S, there exists a residually finite finitely generated group G, such that S is isomorphic to Out(G). During the talk we will discuss various assumptions on G, which give more control over Out(G). In particular, we will show that if, in addition to finite generation and residual finiteness, G has infinitely many ends, then Out(G) is residually finite. We will also discuss other results, treating the situation when G is a non-positively curved group with only one end.

This talk is part of the Algebra and Representation Theory Seminar series.

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