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Let $G$ be a group and $p$ a prime. The subgroup generated by the elements of order different from $p$ is called the Hughes subgroup for exponent $p$. Hughes [3] made the following conjecture: if $H_p\left(G\right)$ is non-trivial, its index in $G$ is at most $p$. There are many articles that treat this problem. In the present Note we examine those of Strauss and Szekeres [9], which treats the case $p=3$ and $G$ arbitrary, and that of Hogan and Kappe [2] concerning the case when $G$ is metabelian, and $p$ arbitrary. A common proof is...