Permutations, Cosets, and Direct Products Flashcards
1
Q
Every permutation is one-to-one function.
A
True
2
Q
Every function is a permutation if and only if it is one to one.
A
False.
3
Q
Every function from a finite set onto itself must be one to one.
A
True
4
Q
Every group G is isomorphic to a subgroup of S↓G.
A
True
5
Q
Every subgroup of an abelian group is abelian.
A
True
6
Q
Sn is not cyclic for any n.
A
False
7
Q
Every element of a group generates a cyclic subgroup of the group.
A
True
8
Q
The symmetric group S¹⁰ has 10 elements.
A
False
9
Q
The symmetric group S³ is cyclic.
A
False
10
Q
Every group is isomorphic to some group of permutation
A
True
