Math Problem Statement

Let G be a group of order 42.

  1. Determine the number of Sylow-7 subgroups of G.

  2. Let H1 ⊆ G be a Sylow-3 subgroup of G. Show that G has a subgroup H2 satisfying

|H2| = 2 and H1 ∩ H2 = {e}.

  1. Prove that G has a subgroup of order 6

Solution

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Math Problem Analysis

Mathematical Concepts

Group Theory
Sylow Theorems
Subgroup Construction

Formulas

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Theorems

Sylow theorems

Suitable Grade Level

Advanced Undergraduate