Yay! Okay, here are my two remaining issues:

If a finite group has only one subgroup of a particular order, how do I know that subgroup is normal? Also, I need a group which has no elements of finite order greater than one, but which has a factor group with all finite elements. Any takers?

(Not that I think any subgroup is abnormal. I would never want to put that kind of pressure on a subgroup, which after all is constantly living in the shadow of the Big G, which is having its own issues about the lingering possibility of being called simple.)

The nice thing about comfort food is that it's actually comforting.

Chow down, ladies.

Okay. For the first one, you have a subgoup N of G that is of order k. Take g in G and n in N such that g^-1*n*g is not in N. Then the group defined by g^-1*n2* g for each n2 in N will be a group of order k (I'm 97% sure - showing it is your job) that isn't N, a nice contradiction.

For the second one, um, I dunno. I'd guess there's some way to show that (Z, +) works, but I'm not sure. Sorry, I'm not so great with this stuff.

I was heading in that direction, but hadn't quite managed to make it into a subgroup of its own. Thank you! Now the second one... rrrrgh. Part of the problem is that I keep getting messed up by the word element -- I understand an element of G, but is an element of the factor group G/H a coset? So that would translate to finding an infinite group with a finite subgroup -- I can do that, I think, but I want to make sure what's being measured here.

Hmm. I'll think on it and get back to you if I tink of something. Maybe do some reviewing of terms. For now, walking back to my apartment, so it'll be a few.

True tales of insanity.

My mom had some medical equipment delivered today, including an IV pole. It came in a few pieces. Mom asked K-Bug to unpack it for her.

K-Bug stood there, looking at the pieces and asked where the ivy was.

Oy!!!!

K-Bug stood there, looking at the pieces and asked where the ivy was.

That's funny!

Just in case you're wondering D., I've decided to go with the factor group G/{e}, because the question says G can't have any elements of finite order >1, but the factor group has to have elements of finite order. No ">1" in that part of the sentence. So I feel like it's looking for something else, but that's what I've come up with.

Now off to spin some bullshit about the history of math in India.

Oh hell. I forgot I hadn't finished another problem. I've gotten myself in a bind over showing that the inner automorphisms of G form a normal subgroup of the group of automorphisms of G under function composition. Damn.

I've gotten myself in a bind over showing that the inner automorphisms of G form a normal subgroup of the group of automorphisms of G under function composition.

Current leader of my list of English Sentences That Make No Sense To Me. All I know is that it sounds bad.