On permutation characters of wreath products

AbstractIt is known that the character rings of symmetric groups Sn and the character rings of hyperoctahedral groups S2≀Sn are generated by (transitive) permutation characters. These results of Young are generalized to wreath products G≀H (G a finite group, H a permutation group acting on a finite set). It is shown that the character ring of G≀H is generated by permutation characters if this holds for G, H and certain subgroups of H. This result can be sharpened for wreath products G≀Sn;if the character ring of G has a basis of transitive permutation characters, then the same holds for the character ring of G≀Sn