Groups of Order 2p Homework Solutions
Suppose p is an odd prime. This homework will classify the groups of order
2p. Most of it works the same as the classication of groups of order 6 = 2 3
done in class.
1. Name two non-isomorphic groups of order 2p, and
MAT 443: Test 1 Solutions
1. (a) Dene group.
A group is a set G with a binary operation such that
i. For all a, b, c G, (a b) c = a (b c)
ii. There exists e G such that for all a G, a e = e a = a.
iii. For all a G, there exists a G such that a a = e.
(b)
Test 2 - Solutions
1. (a) State Lagranges theorem.
If G is a group and H G, then |G| = |H | (G : H ). (Also acceptable is that if G is a nite
group and H is a subgroup of G, then the order of H is a divisor of the order of G.)
(b) State the Fundamental Ho