Recent content by buckeye1973

I had an exam where we were asked to write the lattice for $D_4$, without ever really being shown how to go about doing so. I worked it out since then, but it took a long time and I never understood how we were supposed to be able to do it on the exam. (Other students agreed, I don't know anyone...

OK, thank you. I was thinking along those lines, but had imagined there must be a nicer way. It is good to see it spelled out by someone, so now I have some more confidence that I'm doing things right. I think I have a strategy at least for keeping it all organized, as follows: 1. List all the...

Hi all, I'm looking for basic strategies for identifying the subgroups of a group. I believe I have to use conjugacy classes and cycle types, but I'm not sure how to apply those concepts. Let me pose a specific problem: Let $G$ be a subgroup of the symmetric group $S_5$, with $|G| = 4$. By...

Aha, I see, then. The obvious fact that $y \in yH$ (by the identity in the subgroup $H$) had not come to mind. So my proof concludes: Let $x,y \in G$ such that $x \equiv_H y$. Then $x^{-1}y \in H$, which implies $(x^{-1}y)^{-1} = y^{-1}x \in H$. So $y^{-1}x = h_y$ for some $h_y \in H$. Then...

Hi all, first post, please bear with me! I am trying to understand Lagrange's Theorem by working through some exercises relating to the Orbit-Stabilizer Theorem (which I also do not fully understand.) I think essentially I'm needing to learn how to show cosets are equivalent to other things or...