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arXiv · 2610.35643

Finite groups with exactly 2p + 1 subgroups of order p

Ihechukwu Chinyere·Bernard O. Bainson
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Abstract

Let m_p(G) be the number of elements of order p in a finite group G, p prime. We prove that there is no finite simple group G with m_p(G) = 2p^2-p-1, and that a finite group with this property exists if and only if 2p+1 is prime or 3^f with f an odd prime. This concerns an open problem and extends the classification of finite groups with few elements of prime order.

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Ihechukwu Chinyere, Bernard O. Bainson. 2026-10-26. Finite groups with exactly 2p + 1 subgroups of order p. https://arxiv.org/abs/2610.35643

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