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New posts in group-presentation
Is a HNN extension of a virtually torsion-free group virtually torsion-free?
group-theory
geometric-group-theory
group-presentation
combinatorial-group-theory
free groups: $F_X\cong F_Y\Rightarrow|X|=|Y|$
abstract-algebra
group-theory
group-presentation
Show that any subgroup of a finitely generated abelian group is finitely generated?
abstract-algebra
induction
abelian-groups
group-presentation
combinatorial-group-theory
Is $\langle a,b \mid a^2b^2=1 \rangle$ a semidirect product of $\mathbb{Z}^2$ and $\mathbb{Z}_2$?
group-theory
group-presentation
Can we apply relations in a group presentation one by one?
group-theory
group-presentation
combinatorial-group-theory
Does $A$ have infinite order in $G= \langle A,B \ |\ B A B^{-1} = A^2 \rangle $?
group-theory
representation-theory
group-presentation
geometric-group-theory
Is it possible that pair of isomorphic subgroups of finite group is conjugate in some larger group
abstract-algebra
group-theory
group-isomorphism
group-presentation
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 $G$? [duplicate]
group-theory
group-presentation
Generalisation of the Symmetric Group
group-theory
symmetric-groups
group-presentation
braid-groups
Von Dyck's theorem (group theory)
abstract-algebra
group-theory
group-presentation
Character Table From Presentation
group-theory
representation-theory
characters
group-presentation
combinatorial-group-theory
If we are handed the presentation $\langle i,j,k \mid i^2=j^2=k^2=ijk \rangle$ and nothing more, can we deduce that this is the quaternion group?
group-theory
finite-groups
quaternions
group-presentation
combinatorial-group-theory
Let $G=\langle x, y\mid x^7=y^3= e, yxy^{−1}=e\rangle$. Find $|G|$. Find a group that is isomorphic to $G$. Explicitly state the isomorphism
group-theory
finite-groups
group-presentation
Does this group presentation define a nontrivial group?
group-theory
free-groups
group-presentation
Let $G = \langle x, y \mid x^{7} = y^{3} = e,\; yxy^{−1} = x\rangle$. What is $|G|\,$?
abstract-algebra
group-theory
abelian-groups
group-presentation
combinatorial-group-theory
How "bad" can presentation of the trivial group get?
abstract-algebra
group-theory
reference-request
group-presentation
Presentation of Rubik's Cube group
group-theory
finite-groups
group-presentation
rubiks-cube
Identifying $\langle a,b\mid a^2b^2\rangle$.
group-theory
group-presentation
combinatorial-group-theory
Is almost any group generated by two generators?
group-theory
finite-groups
asymptotics
group-presentation
finitely-generated
Why the group $\langle x,y\mid x^2=y^2\rangle $ is not free?
abstract-algebra
free-groups
group-presentation
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