State Corollary 5.11 about groups of prime order (what property, what does each element satisfy).
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State Corollary 5.11 about groups of prime order (what property, what does each element satisfy).
Corollary 5.11: Every group of prime order is cyclic, and in such a group every element except the neutral element is a generator.
Proof: Only \(1 | p\) and \(p | p\) for \(p\) prime. So for \(a \in G\), either \(\text{ord}(a) = 1\) (meaning \(a = e\)) or \(\text{ord}(a) = p\) (meaning \(a\) generates the whole group; Lagrange).
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State Corollary 5.11 about groups of prime order (what property, what does each element satisfy). (Proof Included)
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State Corollary 5.11 about groups of prime order (what property, what does each element satisfy). (Proof Included)
Corollary 5.11: Every group of prime order is cyclic, and in such a group every element except the neutral element is a generator.
Proof: Only \(1 | p\) and \(p | p\) for \(p\) prime. So for \(a \in G\), either \(\text{ord}(a) = 1\) (meaning \(a = e\)) or \(\text{ord}(a) = p\) (meaning \(a\) generates the whole group; Lagrange).
Field-by-field Comparison
| Field | Before | After |
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| Front | <p>State Corollary 5.11 about groups of prime order (what property, what does each element satisfy).</p> | <p>State Corollary 5.11 about groups of prime order (what property, what does each element satisfy). <i>(Proof Included)</i></p> |