Visual Group Theory, Lecture 4.4: Finitely generated abelian groups

[@kattenelvis1778]

If you're reading this, congratulations! You're halfway through and have made if further than most people.

[@linguisticaparatodos4343]

The presentation given at minute 22:38 is incorrect. In particular, the presentation of Z x Z needs to take into account that the generators commute. If no relation is given, this would be a presentation of the free group with two generators, which is not abelian.

[@matthewmacauley5441]

Yep, thanks for pointing this out, I noticed it the next time I taught from these slides in the classroom. It's been corrected on the slides on the course webpage. Unfortunately, I can't edit KZbin videos. See page 35: www.math.clemson.edu/~macaule/classes/f19_math4120/slides/math4120_slides_section4_h.pdf

[@linguisticaparatodos4343]

@@matthewmacauley5441 You're welcome! The videos are very nice, so it is worth it to comment :)

[@primefactor5417]

These are wonderful lectures on group theory .... please make lectures on advanced group theory

[@fallenangel8785]

Thank you

[@lup-ingenieria]

Thanks for this lecture series!.

[@BlackRose4MyDeath]

These are some very wonderful lectures. I am just wondering one thing, if G is a group isomorphic to Z8 x Z25, is it fair to say that all subgroups of order 8 in G are isomorphic to Z8?

[@monali4423]

@James how so? G is a cyclic group with unique subgroup of order 8 which is Z8 in this case