kabenyuk's user avatar
kabenyuk's user avatar
kabenyuk's user avatar
kabenyuk
  • Member for 6 years
  • Last seen this week
10 votes
Accepted

Suppose $G=\left\langle x, y, t\mid x^7=y^7=t^3=1, txt^{-1}=x^2, tyt^{-1}=y\right\rangle$. Show that $y\in Z(G)$.

9 votes
Accepted

Compact simple group which is not a Lie group

8 votes

Classification of subgroups of $(\mathbb Q,+)$ that are not finitely generated.

7 votes
Accepted

A finite group of order $mn$ with $m,n$ relatively prime, together with subgroups of orders $m, n$.

7 votes

Proof of statement regarding bipartite graphs

7 votes

Examples of a number $d$ that is a divisor of the order of a group $G$, but there is no quotient group $G/N$ whose order is $d$.

7 votes

Example of a non normal subgroup of finite index in an infinite group

6 votes
Accepted

Does every $3$-regular bipartite graph have a $4$-cycle?

6 votes
Accepted

Classification of groups such that the converse to Lagrange holds

6 votes

Find the minimum number of edges in a graph with $3n+1$ vertices if ...

6 votes
Accepted

Showing there is a node in the graph with one and only one edge

6 votes

Let G be a non abelian group with a square-free order. Prove that there are two elements $a,b\in G$ such that $ab\neq ba$ and $ord(a)=ord(b)$.

6 votes
Accepted

Faithful actions of the free group on two generators

5 votes
Accepted

Planar graph K3,3

5 votes
Accepted

Subgroups of index $2$ of $D_3 \times D_3$

5 votes

Number of permutations in the symmetric group $S_n$ composed of $k$ disjoint $m$-cycles

5 votes

Prove that : $f(n) \le \frac{1}{4}(n-1)^2+1 $

5 votes
Accepted

Prove that if $G$ is a finite simple group containing a subgroup $H$ of order $27$, then $|G : H| \ge 9.$

5 votes
Accepted

A group such that all its subgroups are finitely generated

5 votes
Accepted

Find the value of an expression related to the roots of a quadratic polynomial

5 votes

How many planar graphs of vertex degrees all ≥4 are there?, extended (by request of G.M.)

5 votes

An example of a non-diagonalisable matrix in $\mathrm{SL}(n, \mathbb{Z})$ whose eigenvalues don't all have absolute value $1$

5 votes
Accepted

How to find subgroups of a product group containing the diagonal?

4 votes
Accepted

State a necessary and sufficient condition for a finite dimensional vector space $V$ over a field $F$ has precisely one basis.

4 votes

About four points lying on a sphere

4 votes

Proof that a graph with at most $n+2$ edges is planar

4 votes

Let $G$ be generated by $\begin{pmatrix}1&p\\ 0&1\end{pmatrix},\begin{pmatrix}1&0\\ p&1\end{pmatrix}$ for prime $p$. Is $G$ is solvable? A proof.

4 votes
Accepted

Proving or disproving planarity

4 votes
Accepted

$A,B$ are real matrices, similiar in complex field, then they are similar in the real field.

4 votes
Accepted

Number of bipartite graphs given two sets

1
2 3 4 5
14