Let G be a finite group and p be a prime number.Suppose that pr divides the...

Let G be a finite group and p be a prime number.Suppose that pr divides the order of G. Show that G has a proper subgroup of order pr.

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Colby Messinger answered 6 months ago

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Throughout this question, let G be a finite group, let p be a prime, and suppose...

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Let G be finite with |G| > 1. If Aut(G) acts transitively on G − {e} then G ∼= (Z/(p))n for some prime p.

Let G be a finite group and H a subgroup of G. Let a be an...

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Let a be an element of a finite group G. The order of a is the...

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Theorem 2.1. Cauchy’s Theorem: Abelian Case: Let G be a finite abelian group and p be...

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Let (G,·) be a finite group, and let S be a set with the same cardinality...

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Let P be a finite p-group. Show that Φ(P) is the unique normal subgroup of P...

Let P be a finite p-group. Show that Φ(P) is the unique normal subgroup of P minimal such that the corresponding factor group is elementry abelian

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