Skip to main content

All Questions

Filter by
Sorted by
Tagged with
5 votes
1 answer
764 views

Conjugacy classes in $GL_{n}(Z / pZ)$

Let $p$ be a prime number and $G=GL_n ( \mathbb{Z} / p \mathbb{Z} )$. Consider the set $U$ of upper-triangular matrices of $G$ having entries of $1$ on the diagonal. The cardinality of $U$ is $p^{\...
Nourddine Snanou's user avatar
13 votes
1 answer
651 views

The Möbius number of the nonabelian finite simple groups

Let $L$ be a finite lattice with minimum $\hat{0}$ and maximum $\hat{1}$. The Möbius function $\mu$ for $L$ is defined recursively by: for $\forall a,b \in L$ with $a<b$, $\mu(b,b) = 1$ and $\mu(...
Sebastien Palcoux's user avatar
16 votes
1 answer
804 views

Existence of a faithful irreducible representation using Möbius function

Let $G$ be a finite group, $L(G)$ its subgroup lattice and $\mu$ the Möbius function. Consider the Euler totient of $G$ defined as follows: $$ \varphi(G) = \sum_{H \le G}\mu(H,G) |H| $$ Let $X=\{M_1, \...
Sebastien Palcoux's user avatar
5 votes
2 answers
566 views

Orbits of independent sets of the hypercube

How does one enumerate the distinct orbit classes of independent sets of the hypercube modulo symmetries of the hypercubes? The counting of the number of independent sets in an $n$-dimensional ...
AB Balbuena's user avatar