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New posts in finite-groups
Does $A^{-1}A=G$ imply that $AA^{-1}=G$? [closed]
group-theory
finite-groups
infinite-groups
Qualifying Exam Question On Elementary Group Theory
group-theory
finite-groups
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
group-theory
finite-groups
abelian-groups
least-common-multiple
What is this method called - Abelization of a Group.
group-theory
finite-groups
terminology
Finite group is abelian if the representatives of its conjugacy classes commute
abstract-algebra
group-theory
finite-groups
A conjugacy class $C$ is rational iff $c^n\in C$ whenever $c\in C$ and $n$ is coprime to $|c|$.
abstract-algebra
group-theory
finite-groups
representation-theory
Which families of groups have interesting formulas for the number of elements of given order?
abstract-algebra
group-theory
elementary-number-theory
finite-groups
q-analogs
Decomposition of Permutation Representation
finite-groups
representation-theory
permutations
Uniqueness of the direct product decomposition of finite groups
group-theory
finite-groups
Cancellation of Direct Product in Grp
abstract-algebra
group-theory
finite-groups
Prove that a group with exactly two proper nontrivial subgroups is isomorphic to $\mathbb{Z}_{pq}$ or $\mathbb{Z}_{p^3}$.
abstract-algebra
group-theory
finite-groups
An abelian subgroup of symmetric group
abstract-algebra
group-theory
finite-groups
symmetric-groups
How can I compute $\mathrm{Aut}(\mathbb{Z}/4\mathbb{Z}\times\mathbb{Z}/6\mathbb{Z})$?
group-theory
finite-groups
Examples of finite groups that are not a semidirect product
group-theory
finite-groups
Left and right transversals of groups.
group-theory
finite-groups
Calculating the group co-homology of the symmetric group $S_3$ with integer coefficients.
group-theory
finite-groups
group-cohomology
Finite groups of which the centralizer of each element is normal.
group-theory
finite-groups
Show that if $|G|=30$ then $G$ has normal $3$-Sylow and $5$-Sylow
group-theory
finite-groups
solution-verification
normal-subgroups
sylow-theory
Group of order $105$ has a subgroup of order $21$
abstract-algebra
group-theory
finite-groups
Only a solvable group can have 3 Sylow p-subgroups
group-theory
finite-groups
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