All finitely generated free-by-cyclic groups are conjugacy separable, resolving Question 19.41 of the Kourovka Notebook and implying residual finiteness of their outer automorphism groups.
Unipotent linear suspensions of free groups
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Free-by-cyclic groups with coarse medians are algebraically characterized by unbranched blocks in maximal virtually F_n x Z subgroups and excessive linearity of completely split relative train track maps.
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Free-by-cyclic groups are conjugacy separable
All finitely generated free-by-cyclic groups are conjugacy separable, resolving Question 19.41 of the Kourovka Notebook and implying residual finiteness of their outer automorphism groups.
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Characterizing hierarchically hyperbolic free by cyclic groups
Free-by-cyclic groups with coarse medians are algebraically characterized by unbranched blocks in maximal virtually F_n x Z subgroups and excessive linearity of completely split relative train track maps.