I'm working on proving a polynomial-time algorithm I have for the Graph Isomorphism Problem. This is a famous Computer Science problem, but it relates to Group Theory quite a bit!
@@duckymomo7935 The orbit in group theory is the set of elements that can be reached from a given element under the group action. The orbit isn't always a conjugacy class. The conjugacy class involves elements related by conjugation in the group. The conjugacy class of an element g in a group G is the set of all elements in G that are conjugate to g. Two elements g and h in G are conjugate if there exists an element x in G such that h = xgx^{-1}. In some cases, such as certain symmetry groups, the orbit coincides with a conjugacy class, but they aren't the same by definition.
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I'm working on proving a polynomial-time algorithm I have for the Graph Isomorphism Problem. This is a famous Computer Science problem, but it relates to Group Theory quite a bit!
@@asmithgames5926 that’s really cool! Can you explain the problem in more detail?
How does your algorithm work?
nice video, i'd be very interested to see your take on Cayley's theorem
@foobargorch great, it’ll be a pleasure! 😎
I thought you were going to talk about five different fundamental groups of different topological spaces lmao xD. Great video btw!
Cayley`s theorem sure does look like somthing i would look closer onto !
@@victork8708 thanks for letting us know! We will definitely post a video about, since it interests you and other people who commented as well 😎
Yay, another video!)
is the orbit a conjugacy group?
@@duckymomo7935 The orbit in group theory is the set of elements that can be reached from a given element under the group action. The orbit isn't always a conjugacy class. The conjugacy class involves elements related by conjugation in the group.
The conjugacy class of an element g in a group G is the set of all elements in G that are conjugate to g. Two elements g and h in G are conjugate if there exists an element x in G such that h = xgx^{-1}.
In some cases, such as certain symmetry groups, the orbit coincides with a conjugacy class, but they aren't the same by definition.
@@dibeosokay thank you
I love your videos please keep it up
Yeah, it's genial.
Video quality drops at this point: 1:38 and gets back to normal at 1:58.
@@cupatelj52 hi! Thanks for letting us know, but are you sure about that? Cause Sofia and I just checked (in both of our devices) and it works fine…
Looks fine to me. You probably have your video quality set to auto and your connection just slowed down for a moment.