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 $G$?
59898
Elementary manipulation with elements of group
37414
Question on Groups $G=\langle x,y|x^4=y^4=e,xyxy^{-1}=e\rangle$
158074
Cyclic group $G$ with generator $ab$.
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
105910
How to prove that $[G:xHx^{-1}] = [G:H]$ given $H \le G$?
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
142375
Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.
63136
Prove $G$ is Abelian if $N$ is in the centre of $G$ and $G/N$ is cyclic
152741
Cardinal of a group $G$ such that for all $x\in G$ we have $x^2=e$
92692
Prove $3(x^2y+y^2z+z^2x)(xy^2+yz^2+zx^2)\ge xyz(x+y+z)^3$
156319
Show that a group with $|G| = 33$ contains an element of order $3$
62455
Prove Equivalence Relation in G
84501
Proof involving Cyclic group, generator and GCD
94239
Proof that if group $G/Z(G)$ is cyclic, then $G$ is commutative
11957
G is the product of its Sylow subgroups
158490
Prove that $G^{op} \cong G$ when $G^{op}$ is the opposite group of G
46863
Show that $g$ is injective