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In his Habilitationsschrift [3] B. Fischer introduced the concept of a normally embedded subgroup of a finite group. A subgroup of a finite group G is said to be normally embedded in G if each of its Sylow subgroups is a Sylow subgroup of a normal subgroup of G. Meanwhile this concept has become of considerable importance in the theory of finite soluble groups and has been studied by various authors. However, in infinite group theory, normally embedded subgroups seem to have received little attention. The object of this note is to study normally embedded subgroups of locally soluble FC-groups.

Abstract. For a Fitting set ff of a locally soluble FC-group, the existence and local conjugacy of ~-injectors is established, in particular, the locally nitpotent injectors are described. Normally embedded subgroups of locally soluble FC-groups are characterized in terms of Fischer sets.

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