algebra / Group theory

Zhang's Question on Howson and Strongly Howson Groups

A group is Howson if the intersection of any two finitely generated subgroups is finitely generated, and strongly Howson if the rank of that intersection is bounded in terms of the two ranks. Zhang asked whether the two coincide for finitely generated groups. They do not.

9Significance / 100
1Frontier events
0Verification tasks
0Recorded attempts

Temporal state

Current frontier

No reconciled state yet.

Append-only history

Frontier timeline

algebraMay 29, 2026Significance 9/100Registry: unreviewed

Zhang's Question on Howson and Strongly Howson Groups

Prior state unknowndisproved

A group is Howson if the intersection of any two finitely generated subgroups is finitely generated, and strongly Howson if the rank of that intersection is bounded in terms of the two ranks. Zhang asked whether the two coincide for finitely generated groups. They do not.

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Research memory

Claims and attempts

Scoped claims

Source authenticated

A group is Howson if the intersection of any two finitely generated subgroups is finitely generated, and strongly Howson if the rank of that intersection is bounded in terms of the two ranks. Zhang asked whether the two coincide for finitely generated groups. They do not.

Recorded attempts

Evidence graph

Connected research record

No public relationships recorded yet.