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Questions about the branch of algebra that deals with groups.

8 votes

HNN Embedding Theorem for Amenable Groups?

Theorem 2 of Hall, P. On the finiteness of certain soluble groups. Proc. London Math. Soc. (3) 9 1959 595--622. shows that there is a finitely generated solvable group of derived length 3 with a subgr …
Peter Linnell's user avatar
10 votes
Accepted

Finite index subgroups of free groups and torsion-free amenable quotients of free groups

If F is a free group and R is a normal subgroup of F, then I thought it was well-known that F/R' is torsion free (cannot find an explicit reference now, though this is stated just after Lemma 5 of [Fa …
Peter Linnell's user avatar