Finite nilpotent groups coincide with their $2$-closures in all of their faithful permutation representations

Alireza Abdollahi; Majid Arezoomand

doi:10.1142/s0219498818500652

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arXiv · 1611.01634

Finite nilpotent groups coincide with their $2$-closures in all of their faithful permutation representations

Alireza Abdollahi·Majid Arezoomand

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Abstract

Here we show that a finite nilpotent group is 2-closed if and only if it is either cyclic or a direct product of a generalized quaternion group with a cyclic group of odd order.

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Alireza Abdollahi, Majid Arezoomand. 2016-11-05. Finite nilpotent groups coincide with their $2$-closures in all of their faithful permutation representations. https://doi.org/10.1142/s0219498818500652

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