Groups with the same orders of Sylow normalizers as the Mathieu groups

Behrooz Khosravi and Behnam Khosravi

International Journal of Mathematics and Mathematical Sciences, 2005, vol. 2005, 1-5

Abstract:

There exist many characterizations for the sporadic simple groups. In this paper we give two new characterizations for the Mathieu sporadic groups. Let M be a Mathieu group and let p be the greatest prime divisor of | M | . In this paper, we prove that M is uniquely determined by | M | and | N M ( P ) | , where P ∈ Syl p ( M ) . Also we prove that if G is a finite group, then G ≅ M if and only if for every prime q , | N M ( Q ) | = | N G ( Q ′ ) | , where Q ∈ Syl q ( M ) and Q ′ ∈ Syl q ( G ) .

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:243541

DOI: 10.1155/IJMMS.2005.1449

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