Abstract: This paper deals with the singular semilinear elliptic problem where is a smooth bounded domain, and is -symmetric with respect to a subgroup of , , , with , , , is continuous and -symmetric on and is a continuous nonlinearity of lower order satisfying some conditions. Based upon the symmetric criticality principle of Palais and variational methods, we prove several existence and multiplicity results of -symmetric solutions under certain appropriate hypotheses on , and . [Copyright &y& Elsevier]