@vv i'll give that a shot it seems to be what I'm looking for. Thanks for the help!

@vv I've been working on implementing the above solution but it keeps breaking all of my own modules which depend on GroupTheory. The factor approach is very useful for my situation, and I will probably wind up using it. Thank you.

As a side note, do you happen to know how to convert Physics:-`.` expressions to normal `.` expressions? The GroupTheory:-Group function won't accept Physics:-`.` expressions as input so it is proving to be useless.

@Markiyan Hirnyk This is exactly what I was looking for. I thought I had gone through the Physics package to no avail, but apparently the Inverse function was what I really needed! Even just executing

a2*Inverse(a2*Inverse(a1)*a2)*a2

will simplify correctly, without the Simplify() call, but it is handy to have both. Thank you again for the help!

@vv Thank you for the response! I wasn't thinking of `.` in terms of the matrix dot product, so thank you for clarifying the behavior. You are right that in general the inverse may not exist, however I am assuming the inverse elements exists for elements of my finitely presented group. Markiyan Hirnyk's answer is what I was looking for but I appreciate the insight!