For a finite group G, let m(G) denote the set of maximal subgroups of G and π(G) denote the set of primes which divide |G|. In [Arch. Math. 101 (2013), 9–15], it is proven that |m(G)| = |π(G)| when G is cyclic and if G is noncyclic |m(G)| ≥ |π(G)| + p, where p ∈ π(G) is the smallest prime that divides |G|. In this paper, we produce two new lower bounds for |m(G)|, both of which consider all of the primes in π(G).
This paper is a part of the author's Ph.D. thesis at the University of Florida under the direction of Dr. Alexandre Turull. The author wishes to express the deepest appreciation for his continued support. The author would also like to thank the referee for his/her promptness and valuable comments.
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