In this note we answer some questions on \(\text{ LCD }\) group codes posed in de la Cruz and Willems (Des Codes Cryptogr 86:2065–2073, 2018) and (Vietnam J Math 51:721–729, 2023). Furthermore, over prime fields we determine completely the p-part of the divisor of an \(\text{ LCD }\) group code. In addition we present a natural construction of nearly \(\text{ LCD }\) codes.
