Two Step Subgroup Test | Abstract Algebra Exercises

We prove the two-step subgroup test for showing a nonempty subset of a group is a subgroup. We also do a two step subgroup test example, showing the logarithms of positive rationals make a subgroup of the additive reals using the two step test. The test is as follows: If H is a nonempty subgroup of a group G, and if a,b in H implies ab is in H, and a^(-1) is in H, then H is a subgroup of G. #abstractalgebra

All About Subgroups:    • All About Subgroups | Abstract Algebra  
One Step Subgroup Test:    • One Step Subgroup Test | Abstract Alg...  
Finite Subgroup Test:    • Finite Subgroup Test | Abstract Algeb...  
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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