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Let  G  be a finite group and  H  ≤  G . The authors study the structure of finite groups  G  having a subgroup  H  which is maximal in 〈 H ,  H g  〉 for some  g  ∈  G . Some results on the structure of 〈 H ,  H g  〉 and  G  are set up. Especially, a generalization of Baer′s theorem is established.

A note on the structure of a finite group G having a subgroup H maximal in 〈 H , H g 〉