Podcast
Play an AI-generated podcast conversation about this lesson
Questions and Answers
What is the defining characteristic of a cyclic group?
What is the defining characteristic of a cyclic group?
- Has an infinite number of elements
- Contains elements that are not powers of the generator
- Generated by multiple elements
- Generated by a single element (correct)
If a group G can be expressed as G=g, what does this notation signify?
If a group G can be expressed as G=g, what does this notation signify?
- G is not cyclic
- G contains no subgroups
- G is generated by the element g (correct)
- G has an infinite order
What is the order of a cyclic group defined as?
What is the order of a cyclic group defined as?
- Order the group was created in
- Number of elements in the group (correct)
- Number of times the generator has been multiplied by itself
- Number of distinct generators in the group
If a group can be generated by one element but contains other elements not expressible as powers of the generator, is it cyclic?
If a group can be generated by one element but contains other elements not expressible as powers of the generator, is it cyclic?
Signup and view all the answers
In a cyclic group, what can be said about every subgroup?
In a cyclic group, what can be said about every subgroup?
Signup and view all the answers
Are all subgroups of a cyclic group unique in their order?
Are all subgroups of a cyclic group unique in their order?
Signup and view all the answers
How do isomorphism and cyclic groups relate?
How do isomorphism and cyclic groups relate?
Signup and view all the answers
