Finite Subgroup Test | Abstract Algebra Exercises

We prove the finite subgroup test for showing a nonempty finite subset of a group is a subgroup. We also do a finite subgroup test example, showing the set generated by 2 is a subgroup of the additive integers mod 10 using the finite subgroup test. The test is as follows: If H is a nonempty and finite subset of a group G that is closed under the operation fo G, then H is a subgroup. #abstractalgebra

All About Subgroups:    • All About Subgroups | Abstract Algebra  
Order of Group Elements:    • Order of Elements in a Group | Abstra...  
Finite Order Elements Have n Distinct Powers:    • Proof: Finite Order Elements Have n D...  
Two Step Subgroup Test:    • Two Step Subgroup Test | Abstract Alg...  
One Step Subgroup Test:    • One Step Subgroup Test | Abstract Alg...  
One Step, Two Step, and Finite Subgroup Tests:    • Two Step, One Step, and Finite Subgro...  

Abstract Algebra Course:    • Abstract Algebra  
Abstract Algebra Exercises:    • Abstract Algebra Exercises  

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