On a bound of Cocke and Venkataraman
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AbstractLet G be a finite group with exactly k elements of largest possible order m. Let q(m) be the product of $$\gcd (m,4)$$ gcd ( m , 4 ) and the odd prime divisors of m. We show that $$|G|\le q(m)k^2/\varphi (m)$$ | G | ≤ q ( m ) k 2 / φ ( m ) where $$\varphi $$ φ denotes Euler’s totient function. This strengthens a recent result of Cocke and Venkataraman. As an application we classify all finite groups with $$k<36$$ k < 36 . This is motivated by a conjecture of Thompson and unifies several partial results in the literature.
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2016 ◽
Vol 15
(03)
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pp. 1650057
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1968 ◽
Vol 8
(1)
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pp. 49-55
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2009 ◽
Vol 08
(03)
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pp. 389-399
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1969 ◽
Vol 10
(3-4)
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pp. 359-362
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