I've been playing a little with group definitions to see what kind of things I can make up. I'm struggling to prove that this group is finite. Can anyone point me in the right direction?
2026-04-03 22:38:10.1775255890
Is $\langle a,b\; |\;a^7 = 1, ab = b^3a^3\rangle$ finite?
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This group is infinite, but the proof was a lengthy computer calculation which proved it automatic and found the automatic structure, so I am afraid you might not find that totally satisfactory. The order of $b$ is indeed infinite.