Abstract
Let 𝒜 = (A 1, A 12, A 2) be a locally D 8 amalgam with a finite completion G. Suppose that A 1 ∈ Syl 2(G). We show that under these conditions |A 1| ≤25, or N A 1 (A 12) is Abelian. As applications of our results, we determine all the finite completions G, up to O(G), in the case where N A 1 (A 12) is non-Abelian.
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2000 Mathematics Subject Classification:
ACKNOWLEDGMENT
We are grateful to the referee, whose comments have improved the article.
Notes
The authors are grateful to Sergey Shpectorov for suggesting this problem under this hypothesis.
Communicated by A. Turull.