On the orders of the non-Frattini elements of a finite group
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Let G be a finite group and let \(p_1,\dots ,p_n\) be distinct primes. If G contains an element of order \(p_1 \cdots p_n,\) then there is an element in G which is not contained in the Frattini subgroup of G and whose order is divisible by \(p_1 \cdots p_n.\)
KeywordsPrime graph Non-Frattini elements Non-Frattini prime graph Generating sets.
Mathematics Subject Classification20D60
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