Appendix to 'Groups of units of orders in Q-algebras'

In the paper 'Groups of units of orders in Q-algebras' by A.L.S. Corner, the following result is proved: A finite group G is realisable as the group of units of an order in a Q-algebra if and only if G is a C2C4C6QDB-group and either (a) G has a direct factor of order 2, or (b) G admits a direct decomposition G=G0 7G1 7 ef 7Gr, where G1,\u2026,Gr are B-blocks and G0 is a C4QD-group which may be embedded as a subdirect product of copies of C4, Q, D in such a way that it contains the diagonal involution 121. The author remarks that the final condition relating to the diagonal involution is not very pretty. He believes that it could be replaced by a more desirable requirement that there exists an element g0 of order 4 in G such that CG(g0) is a 2-group. In the appendix by Federico Menegazzo, the proof of the "more desirable'' requirement is provided