Rawr means ily in dinosaur.

FIXED


parenthesis were optional, i decided to change that

PEMDAS.

For the purposes of this question, we define a Dihedral Group to be a group D = (x , y) where x and y are distinct involutions

1. Classify all abelian dihedral groups.

2. Let z = xy.

i. Show that zx = zy = z−1 and deduce that H = (z) is a normal subgroup of D.
ii. Prove that xH = yH, and deduce that G | H is cyclic of order 1 or 2.

ya ya whatever your wrong, i win.

wtfx is that -____o

1. x and y are distinct elements of order 2. Let z = xy which is clearly not an element of {1; x; y}.
Now G = {1; x; y; z} is closed under multiplication and z^2 = 1 so it is also closed under inversion.
Thus G is a group of size 4, and has the following multiplicative structure:
the product of any pair of dierent non-identity elements is the third non-identity element.

Group Theory, bro.
Don't you know anything?

E: TS can I borrow 5 fg?

This post was edited by nerobellum on Sep 15 2010 06:16pm

nope.



lost atm
topic changed to ponies
Discuss.

This post was edited by TheShattered on Sep 15 2010 06:17pm

I like them there fluffy and fun