CORRIGENDUM: REPLACEMENT OF FACTORS BY SUBGROUPS IN THE FACTORIZATION OF ABELIAN GROUPS

Extract

The above-titled paper of mine appeared in the Bulletin of the London Mathematical Society, 32 (2000) 297–304. Regrettably, there is a careless error in the proofs of Theorems 6 and 8. In line 6 of the proof of Theorem 6, it is claimed that a certain subset must be a subgroup. For this to hold, the subset must contain the zero element. This need not be the case; the true deduction is that the subset is a coset, say $M+h$, of a subgroup $M$. Now $M$ and $M+h$ contain the same number of elements, and so the deduction that $M$ has $p$ elements is still correct.