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1. Let a and b be elements of a group G. Prove that if a E< b>, then < a >C< b >. 2. Let a and b be elements of a finite group G. Prove that:

1. Let a and b be elements of a group G. Prove that if a E< b>, then < a >C< b >. 2. Let a and b be elements of a finite group G. Prove that:

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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1. Let \( a \) and \( b \) be elements of a group \( G \). Prove that if \( a \in \langle b \rangle \), then \(\langle a \rangle \subseteq \langle b \rangle \). 2. Let \( a \) and \( b \) be elements of a finite group \( G \). Prove that:
Transcribed Image Text:1. Let \( a \) and \( b \) be elements of a group \( G \). Prove that if \( a \in \langle b \rangle \), then \(\langle a \rangle \subseteq \langle b \rangle \). 2. Let \( a \) and \( b \) be elements of a finite group \( G \). Prove that:
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