I love how every theorem/demonstration in group theory has a proof which is easy to follow and fits in half a page. I may not have thought of the concept of "center of a group", but once you tell me what it is, I immediately ask myself "is this a subgroup?" and come up with a proof in a few minutes. This *is* going to continue to be true, isn't it? Although when introduced to a new concept, sometimes the things that occur to me to prove turn out not to be true: All orbits are the same size. All members of a given orbit have the same stabilizer. (I can prove this if the stabilizer is a *normal* subgroup. I presume it to be false in general, but I haven't found a counterexample.)
This one is pretty easy. The Orbit and stabilizers were very hard. So , my deduction proving associativity for arbitrary sets is more difficult if conditions weren't inherited. Here the associativity is inherited.
nicely explained. great video👍
Great explanation, intuitive and informative!!!
I love how every theorem/demonstration in group theory has a proof which is easy to follow and fits in half a page. I may not have thought of the concept of "center of a group", but once you tell me what it is, I immediately ask myself "is this a subgroup?" and come up with a proof in a few minutes.
This *is* going to continue to be true, isn't it?
Although when introduced to a new concept, sometimes the things that occur to me to prove turn out not to be true:
All orbits are the same size.
All members of a given orbit have the same stabilizer. (I can prove this if the stabilizer is a *normal* subgroup. I presume it to be false in general, but I haven't found a counterexample.)
This one is pretty easy. The Orbit and stabilizers were very hard. So , my deduction proving associativity for arbitrary sets is more difficult if conditions weren't inherited. Here the associativity is inherited.
See what I get for you tomorrow ok who are the best players of all-time leading