Correction to: “Bifurcation of operator equations with unbounded linearized part”
David Westreich · Pacific Journal of Mathematics · 1976
My recent paper "On Groups with a Single Involution" in the last volume of this journal makes, in the proof of Theorem II, the erroneous claim that A 7 has no nonsplit extension of degree 2. In fact, the Schur multiplier for this group is cyclic of order 6 and so A 7 admits a unique nonsplit extension (call it G) of degree 2. In the context of that proof what is required is that G shall have no absolutely irreducible representation which is both real and faithful.Seeing that this is so is a matter of direct computation which, while lengthy, is straightforward (involving inducing from the nonsplit extension of degree 2 of A 5 and A 6 ) and reveals that all the absolutely irreducible, faithful representations of G are of the second kind, except for a complex conjugate pair which is of the third kind.Theorem II, consequently, stands.Correction to COMPACTLY COGENERATED LCA GROUPS D. L. ARMACOST Volume 65 (1976), 1-12 Added in proof.The group Q has been inadvertently omitted from the list of groups appearing in Theorem 6.1.It arises because the compact open subgroup 0 in the proof could be trivial, in which case G is discrete.This change should also be noted in the abstract.