## Abstract

A finite group

*G*satisfies the one-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes*m*and*n*are either equal or have common divisor a prime power. Taeri conjectured that an insoluble group satisfying this condition is isomorphic to*S*×*A*where*A*is abelian and*S ∼= P SL*for_{2}(q)*q*∈ {4, 8}. We confirm this conjecture.Original language | English |
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Pages (from-to) | 13-19 |

Journal | International Journal of Group Theory |

Volume | 6 |

Issue number | 3 |

Publication status | Published - Sep 2017 |