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

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.

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