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.

It is. It's very bad. Cause, dammit, f(gf'(x)g') is not like gxg', no matter how hard I try to make it be!

I'm all tense and pissy.

With the weight I lost I'm now able to wear my grandfather's cashmere coat. It's beautiful and finely made (likely a hand me-down from a parishioner) and I needed to have the lining patched because it was haniging down in the back

they wanted to replace it, I said, no patch it... I knew the lining was nicer quality than anything they'd have and I wanted to preserve the labels and stuff

I have it back. one of the labels is missing [link] like that, said 'cashmere' and now I'm all pissy and feeling like I should have researched first (turns out Hickey Freeman IS quite nice and still exists)

So, tomorrow I'll go to the drycleaner but I'm sure the label was thrown out yesterday. And I"m cranky and antsy about this, unreasonably stressed.

Oh, and yeah, I'm completly aware that I'm just missing the hell out of my grandfather and projecting it onto his coat but that doesn't seem to be relieving the pissy stressy at all.