Cyclically presented groups as Labelled Oriented Graph groups

We use results concerning the Smith forms of circulant matrices to identify when cyclically presented groups have free abelianisation and so can be Labelled Oriented Graph (LOG) groups. generalize a theorem Odoni Cremona show that for fixed defining word, whose corresponding representer polynomial has an irreducible factor is not cyclotomic equal ±t, there are at most finitely many n which n-generator group abelianisation. classify Campbell Robertson's generalized Fibonacci H(r,n,s) LOG Sieradski prove amongst Johnson Mawdesley's type, only ones Gilbert-Howie H(n,m). conjecture if group, then it this in certain cases (in particular, m, false n). obtain necessary conditions connected terms apply them Prishchepov