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Finite-groups
New post in Finite-groups
Fundamental theorem of Finitely generated abelian groups
August 1st, 2022
finite-groups
abstract-algebra
group-theory
Why is the Converse to Lagrange's Theorem False?
August 1st, 2022
abstract-algebra
finite-groups
group-theory
Describe all extensions of the identity map of $\mathbb{Q}$ to an isomorphism mapping $\mathbb{Q}(\sqrt[3]{2},\sqrt{3})$
April 9th, 2020
group-theory
abstract-algebra
ring-theory
finite-groups
Prove if any group has order 9, then it is abelian.
September 20th, 2020
abstract-algebra
abelian-groups
finite-groups
group-theory
Prove that in any group an element and its inverse have same order.
August 1st, 2022
abstract-algebra
finite-groups
cyclic-groups
How can you tell whether two groups are homomorphic/isomorphic?
November 3rd, 2020
group-isomorphism
group-homomorphism
abelian-groups
finite-groups
group-theory
Non-isomorphic abelian groups of order $19^5$
August 1st, 2022
group-theory
finite-groups
abelian-groups
abstract-algebra
Examples of groups that are not rings
October 8th, 2020
finite-groups
Tensor product of two irreducible representations is not irreducible
December 12th, 2020
abstract-algebra
representation-theory
finite-groups
group-theory
examples-counterexamples
How many elements in this group - Q8?
January 18th, 2020
abstract-algebra
linear-algebra
finite-groups
group-theory
Number of elements in conjugacy class of S6 of cycle type [1,2,3]
April 18th, 2020
combinatorics
symmetric-groups
finite-groups
Let $G$ be a group of order $27.$ If $G$ is not abelian, then $|Z(G)|=3,$ where $Z(G) = \{z \in G: zg=gz, \forall g \in G\}$
August 1st, 2022
proof-verification
group-theory
finite-groups
Give an example of three different groups with eight elements
September 18th, 2020
abstract-algebra
finite-groups
|ab|=lcm(|a|,|b|) in an abelian group
October 10th, 2020
abelian-groups
finite-groups
group-theory
abstract-algebra
least-common-multiple
Number of elements of order $11$ in group of order $1331$
July 9th, 2020
abstract-algebra
sylow-theory
finite-groups
group-theory
Group Theory: How do I determine if an element generates a group?
May 6th, 2020
finite-groups
group-theory
Question about upper central series of a group
October 22nd, 2020
solvable-groups
group-theory
abstract-algebra
finite-groups
Quotient groups of D10
December 4th, 2020
group-theory
finite-groups
Prove that the total number of subgroups of a finite cyclic group $G=\langle a \rangle$ such that $o(G)=n$ is the number of divisors of $n$.
October 29th, 2020
abstract-algebra
finite-groups
group-theory
cyclic-groups
Let $G$ be a cyclic group of order $12$ generated by $a$ and $H$ be a subgroup of $G$ generated by $a^4$. Find the distinct left cosets of $H$ in $G$.
March 11th, 2020
abstract-algebra
group-theory
finite-groups
Find a group of order 60 with subgroup of all possible orders
February 15th, 2021
finite-groups
group-theory
How does one find all elements of the commutator subgroup?
October 26th, 2020
symmetry
finite-groups
group-theory
Why can't G/Z(G) be nontrivial and cyclic?
March 20th, 2020
abstract-algebra
group-theory
finite-groups
How to show every group of order $12$ is solvable?
March 10th, 2020
finite-groups
proof-verification
group-theory
Find all abelian groups of order 60
August 1st, 2022
abstract-algebra
group-theory
finite-groups
Definition of the coset?
November 5th, 2020
finite-groups
group-theory
abstract-algebra
A difficulty in understanding that $A_4$ has no subgroup of order 6.
February 18th, 2020
abstract-algebra
symmetric-groups
permutations
finite-groups
group-theory
Prove that a finite Abelian group $G$ is not cyclic if and only if it contains a subgroup isomorphic to $\mathbb{Z}_p\times\mathbb{Z}_p$
August 1st, 2022
group-theory
finite-groups
cyclic-groups
Classify the abelian groups of order 81, 144 and 216
August 1st, 2022
group-theory
abelian-groups
finite-groups
How does one prove U(100) is not cyclic without computing the order of any element?
August 1st, 2022
abstract-algebra
group-theory
finite-groups
cyclic-groups
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