Algebra/Chapter 27/Exercises: Difference between revisions
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imported>GoreyCat Created page with "==Conceptual Questions== ==Exercises== ===Section 27.1=== ===Section 27.2=== '''<u>27.1</u>''' Assume that <nowiki>*</nowiki> is a binary operation on the set S. Prove the following statements. ===Section 27.3=== '''<u>27.2</u>''' Let <math>G</math> be a group. Prove that the identity element <math>e \in G</math> is unique. Also prove that every element <math>x \in G</math> has a unique inverse, indicated by <math>x^{-1}</math>. ===Section 27.4=== ===Section 27.5=== =..." |
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Latest revision as of 00:18, 1 January 2025
Conceptual Questions
Exercises
Section 27.1
Section 27.2
27.1 Assume that * is a binary operation on the set S. Prove the following statements.
Section 27.3
27.2 Let be a group. Prove that the identity element is unique. Also prove that every element has a unique inverse, indicated by .