Finite groups with Quaternion Sylow subgroup

Abstract

In this paper we show that a finite group G with Quaternion Sylow 2-subgroup is 2-nilpotent if, either 3 |G| or G is solvable and the order of its Sylow 2-subgroup is strictly greater than 16. Mathematical subject classification (2010). 20D99, 20E45. Manuscript received 7th October 2020, revised 11th October 2020 and 13th October 2020, accepted 13th October 2020.