General question about orbits (group theory)

Thread starter linda300
Start date Apr 30, 2012
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General Group theory Orbits Theory

AI Thread Summary

An element of a G-set with an orbit consisting solely of itself, such as Orbit(e) = {e}, represents an orbit of size 1. These size 1 orbits are indeed valid but are often overlooked in discussions about group actions. They can be ignored in certain contexts, particularly when focusing on non-trivial orbits that contribute more significantly to the structure of the group. An example of when these orbits might be disregarded is in applications where only the action of the group on larger sets is relevant. Understanding the role of size 1 orbits can enhance comprehension of group theory dynamics.

Apr 30, 2012

linda300

Hi everyone,

I was just wondering if you have an element of a G-set which has an orbit of only itself,

Say Orbit(e) = {e}, in the set of permutations where G is the same order group of permutations and the operation is conjugation.

This is an Orbit of size 1 correct?

I was just wondering if these size Orbits are often ignored?

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Apr 30, 2012

Office_Shredder

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Can you give an example of when you ever ignore these orbits?

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