Finite group generated by two elements; what can we say about another element?
8742
Examples and further results about the order of the product of two elements in a group
152820
Every element of a group has order $2$. Why, intuitively, is it abelian?
126426
Does every infinite finitely generated group contains an element of infinite period?
13355
Product of elements of a finite abelian group
82037
Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$?
87534
Finitely generated group which is not finitely presented
92672
Number of elements which are cubes/higher powers in a finite field.
147512
Is there difference between finitely presented groups and finitely generated groups?
5089
An element of a group has the same order as its inverse
156247
Question about permutations and cycles (Groups and Symmetries)
58076
Subgroup generated by a set
933
How many groups exist with order $n$ (two isomorphic groups are treated as the same group)
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
84132
Number of preimages of a group element under a homomorphism.
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
21568
Maximal order of an element in a symmetric group
46687
Elements of $GL_{2}(\mathbb{Z})$ of finite order