Abstract

In this paper, we present a general construction of 3-transposition groups as automorphism groups of vertex operator algebras. Applying to the moonshine vertex operator algebra, we establish the Conway-Miyamoto correspondences between Fischer 3-transposition groups F i 23 \mathrm {Fi}_{23} and F i 22 \mathrm {Fi}_{22} and c = 25 / 28 c=25/28 and c = 11 / 12 c=11/12 Virasoro vectors of subalgebras of the moonshine vertex operator algebra.

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