Metrizability of hereditarily normal compact like groups

Inspired by the fact that a compact topological group is \nhereditarily normal if and only if it is metrizable, we prove that various \nlevels of compactness-like properties imposed on a topological group G \nallow one to establish that G is hereditarily normal if and only if G is \nmetrizable (among these properties are locally compactness, local minimality \nand \\omega-boundedness). This extends recent results from [4] in the \ncase of countable compactness.