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Abstract-algebra
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Cyclic group of order 15 and cosets
October 28th, 2020
abstract-algebra
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
group-theory
abstract-algebra
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
finite-groups
abstract-algebra
cyclic-groups
group-theory
Inverse of the element in the multiplicative group
August 1st, 2022
abstract-algebra
group-theory
Proving the Trichotomy Property
January 1st, 2021
real-analysis
analysis
proof-writing
abstract-algebra
Expression of the number of distinct necklaces with $m$ beads of $n$ different colors.(rotations don't count)
August 1st, 2022
abstract-algebra
combinatorics
group-theory
permutations
Prove $o(u^{-1})=o(u)$ for all $u \in G$ and $o(uh)=o(hu)$ for all $u,h \in G$.
August 1st, 2022
abstract-algebra
group-theory
Partition of a set induced by an equivalence relation
August 1st, 2022
abstract-algebra
elementary-set-theory
Proving some polynomials are irreducible using Eisenstein's criterion
August 1st, 2022
abstract-algebra
irreducible-polynomials
factoring
ring-theory
polynomials
Show that Pn is an (n+1)-dimensional subspace
February 8th, 2020
linear-algebra
abstract-algebra
If a group has no subgroups other than the identity and itself, then it is finite and is of prime order
February 8th, 2020
abstract-algebra
group-theory
Prove that there do not exist nonzero integers $a$ and $b$ such that $a^2=3b^2$.
December 19th, 2020
abstract-algebra
Finding ring homomorphisms.
May 13th, 2020
abstract-algebra
Determining automorphisms of this extension
August 1st, 2022
extension-field
galois-theory
field-theory
abstract-algebra
Symmetries of letter H
August 1st, 2022
abstract-algebra
Dimension of a vector space of polynomials in 3 variables of degree $d$ over $\mathbb{R}$
May 2nd, 2020
vector-spaces
polynomials
abstract-algebra
Is the coordinate ring $\mathbb{C}[x,y]/(x^2+y^2-1)$ or the ring $\mathbb{C}[t,t^{-1}]$ unique factorization domains?
August 1st, 2022
commutative-algebra
abstract-algebra
unique-factorization-domains
Nilpotent element in $\mathbb{Z}/12\mathbb{Z}$ - Ideal
August 1st, 2022
abstract-algebra
ideals
nilpotence
Different right / left identity and two sided identity element
August 1st, 2022
abstract-algebra
monoid
Show that the set of all elements $a$ of a group $G$ such that $ax=xa$ for every element of $x$ of $G$is a subgroup of $G$.
May 13th, 2020
group-theory
abstract-algebra
Find the multiplicative inverses of each nonzero element of the field $Z/(5), Z/(11), Z/(17).$
August 1st, 2022
equivalence-relations
abstract-algebra
$G$ is a finite group of permutations of the set $X$. Suppose $G$ acts transitively on $X$. Then $X$ is a finite set, and $|X|$ divides $|G|$.
October 18th, 2020
group-theory
abstract-algebra
If every cyclic subgroup of a group G be normal in G, prove that every subgroup of G is normal in G.
August 1st, 2022
abstract-algebra
group-theory
cyclic-groups
normal-subgroups
Showing that the diagonal is a subgroup
October 17th, 2020
abstract-algebra
group-theory
showing that a group of order $p^n$ has an element of order $p$
January 29th, 2020
abstract-algebra
Determine whether 2 elements represent the same left H-coset
October 24th, 2020
group-theory
abstract-algebra
Group Theory Inverse Proof
October 21st, 2020
abstract-algebra
group-theory
inverse
Show that number of elements in $(Z/nZ)^*$ is $\phi (n)$
August 1st, 2020
abstract-algebra
Maximal Ideal in a commutative ring with unit element
August 17th, 2020
maximal-and-prime-ideals
abstract-algebra
Prove that the ring $(\Bbb Z_n, +_n, \cdot_n)$ is a commutative ring with unity
September 21st, 2020
ring-theory
abstract-algebra
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