On the number of maximal subgroups of a finite solvable group |
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Authors: | Benjamin Newton |
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Affiliation: | 1.Beloit College,Beloit,USA |
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Abstract: | For a finite solvable group G and prime number p, we use elementary methods to obtain an upper bound for mathfrak mp(G){mathfrak {m}_{p}(G)} , defined as the number of maximal subgroups of G whose index in G is a power of p. From this we derive an upper bound on the total number of maximal subgroups of a finite solvable group in terms of its order. This bound improves existing bounds, and we identify conditions on the order of a finite solvable group under which this bound is best possible. |
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