In this work it is shown that the direct product of two Meldrum groups does not satisfy the normalizer condition. It is not known yet if the same result holds true for any two HM-groups.
ASAR, A. O. and ATLIHAN, S. (1996) "A PROPERTY OF MELDRUM GROUPS," Turkish Journal of Mathematics: Vol. 20: No. 2, Article 10. Available at: https://journals.tubitak.gov.tr/math/vol20/iss2/10