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: https://youtu.be/bI6ffidl0hA Order of Group Elements: https://youtu.be/uOq5WJItFu4 Finite Order Elements Have n Distinct Powers: https://youtu.be/ErhT16Ja-RE Two Step Subgroup Test: https://youtu.be/-R8p6xpBLJ8 One Step Subgroup Test: https://youtu.be/jNlgbo9V-98 One Step, Two Step, and Finite Subgroup Tests: https://youtu.be/poQXf90tcFM Abstract Algebra Course: https://www.youtube.com/playlist?list=PLztBpqftvzxVvdVmBMSM4PVeOsE5w1NnN Abstract Algebra Exercises: https://www.youtube.com/playlist?list=PLztBpqftvzxVQNtNnXeHB_1yquKUY98Xz ◉Textbooks I Like◉ Graph Theory: https://amzn.to/3JHQtZj Real Analysis: https://amzn.to/3CMdgjI Abstract Algebra: https://amzn.to/3IjoZaO Linear Algebra: https://amzn.to/43xAWEz Calculus: https://amzn.to/3PieD1M Proofs and Set Theory: https://amzn.to/367VBXP (available for free online) Statistics: https://amzn.to/3tsaEER Discrete Math: https://amzn.to/3qfhoUn Number Theory: https://amzn.to/3JqpOQd ★DONATE★ ◆ Support Wrath of Math on Patreon for early access to new videos and other exclusive benefits: https://www.patreon.com/join/wrathofmathlessons ◆ Donate on PayPal: https://www.paypal.me/wrathofmath Thanks to Loke Tan, Matt Venia, Micheline, Doug Walker, Odd Hultberg, Marc, Roslyn Goddard, Shlome Ashkenazi, Barbora Sharrock, Mohamad Nossier, Rolf Waefler, Shadow Master, and James Mead for their generous support on Patreon! Outro music is mine. You cannot find it anywhere, for now. Follow Wrath of Math on... ● Instagram: https://www.instagram.com/wrathofmathedu ● Facebook: https://www.facebook.com/WrathofMath ● Twitter: https://twitter.com/wrathofmathedu My Math Rap channel: https://www.youtube.com/channel/UCQ2UBhg5nwWCL2aPC7_IpDQ/featured