Cyclic Groups Flashcards
1
Q
T or F
Every cyclic group is abelian.
A
T
2
Q
T or F
Every abelian group is cyclic.
A
F
3
Q
T or F
Q under addition is a cyclic group.
A
F
4
Q
T or F
Every element of every cyclic group generates the group.
A
F
5
Q
T or F
There is at least one abelian group of every finite order >0.
A
T
6
Q
T or F
Every group of order<-4 it s cyclic.
A
F
7
Q
T or F
All generators of Z20 are prime numbers.
A
F
8
Q
T or F
If G and Gā are groups, then G^Gā is a group.
A
F
9
Q
T or F
If H and K are subgroups of a group G, then H^K is a group.
A
T
10
Q
T or F
Every cyclic group of order>2 has at least two distinct generators.
A
T
