Why does not generator of multiplicative group generate all the members of group?
115969
Amount of generators for cyclic group and Euler's function
29717
Not sure how to go about this group theory proof
78867
Python generator that groups another iterable into groups of N
133497
Group Membership Test for Permutations
14139
$(12)$ and $(123\dots n)$ are generators of $S_n$
10816
Infinitely generated subgroup of a finitely one (weird)
53357
Cyclic Group Generators of Order $n$
115574
Finitely presented group with fewer relations than generators.
26572
Does the Symmetric difference operator define a group on the powerset of a set?
102912
Subgroups of finitely generated groups are not necessarily finitely generated
121707
Generating Elements of Galois Group
123482
How to compute $\mathbb{Z}_n^*$, the unit group of the integers modulo $n$?
79380
How to find the order of a group generated by two elements?
138279
Multiplicative order and powers
126590
Why is the multiplicative group of a finite field cyclic?
156463
The complement of a proper subgroup generates the whole group
67926
$S_n$ is generated by elements of the form $(1k)$