The most important comment on this paper is
in a footnote on the title page.
Apart from that, a few more are in order. Shortly after the paper
was published, Prof. Zvonimir Janko contacted us to make us aware of a flaw in
the exposition of the proof of Theorem B. Indeed,
Lemma 2.8, as it appears in the paper, is not fully
correct. A minor change allows us to recover its original version and then the
original proof of the theorem; this is
explained in detail in a correction note.
Many thanks to Prof. Janko for spotting the flaw.
Prof. Janko also informed us that he has been working on
the same class of groups discussed in part (i) of Theorem B (2-groups with
subgroup breadth 1). His results are contained in an upcoming paper, submitted
while ours was in the process of publication. The review in Zentralblatt
für Mathematik of our paper also refers to work by J.P. Bohanon.
What we found is an abstract of
his PhD
thesis (Washington University in St. Louis, 2009), including
the same result as our Theorem B.
Finally, the paper contains a couple of assertions whose proof we did not feel worth
reproducing in print (see the paragraph following Lemma 2.8).
For the convenience of anybody interested in them, their proofs are in
another note in this site.
The most important comment on this paper is in a footnote on the title page.
Apart from that, a few more are in order. Shortly after the paper was published, Prof. Zvonimir Janko contacted us to make us aware of a flaw in the exposition of the proof of Theorem B. Indeed, Lemma 2.8, as it appears in the paper, is not fully correct. A minor change allows us to recover its original version and then the original proof of the theorem; this is explained in detail in a correction note. Many thanks to Prof. Janko for spotting the flaw.
Prof. Janko also informed us that he has been working on the same class of groups discussed in part (i) of Theorem B (2-groups with subgroup breadth 1). His results are contained in an upcoming paper, submitted while ours was in the process of publication. The review in Zentralblatt für Mathematik of our paper also refers to work by J.P. Bohanon. What we found is an abstract of his PhD thesis (Washington University in St. Louis, 2009), including the same result as our Theorem B.
Finally, the paper contains a couple of assertions whose proof we did not feel worth reproducing in print (see the paragraph following Lemma 2.8). For the convenience of anybody interested in them, their proofs are in another note in this site.
Dismiss