Related papers: Sylow branching coefficients and hook partitions

Let $p$ be any prime. We determine precisely those irreducible characters of symmetric groups which contain at most $p$ distinct linear constituents in their restriction to a Sylow $p$-subgroup, answering a question of Giannelli and…

We study the restriction to Sylow subgroups of irreducible characters of symmetric groups. In particular, we focus our attention on constituents of degree greater than 1. Our main result is a wide generalization of Theorem 3.1 of Giannelli…

Let $p\ge 5$ be a prime and let $n$ be a natural number. In this article we describe the irreducible constituents of the induced characters $\phi\big\uparrow^{\mathfrak{S}_n}$ for arbitrary linear characters $\phi$ of a Sylow $p$-subgroup…

We restrict irreducible characters of alternating groups of degree divisible by $p$ to their Sylow $p$-subgroups and study the number of linear constituents.

Let $p\ge 5$ be a prime and let $P$ be a Sylow $p$-subgroup of a finite symmetric group. To every irreducible character of $P$ we associate a collection of labelled, complete $p$-ary trees. The main results of this article describe Sylow…

This note presents a procedure to determine the reduction of the irreducible and the induced characters of the symmetric group in terms of the irreducible and induced characters of the hyperoctahedral group Key Words: Symmetric Group,…

We construct a natural bijection between odd-degree irreducible characters of S_n and linear characters of its Sylow 2-subgroup P_n. When n is a power of 2, we show that such a bijection is nicely induced by the restriction functor. We…

Let $G$ be a finite group and $p$ a prime. We establish an upper bound for the derived length of a Sylow $p$-subgroup of $G$ in terms of the number of irreducible characters of $G$ whose degrees are divisible by $p$. We also prove that if…

We classify Sylow $p$-subgroups of finite groups whose principal $p$-blocks have precisely six ordinary irreducible characters.

The permutation matrices form a subgroup of $\text{GL}_n(\mathbb{C})$ that is isomorphic to the symmetric group $S_n$. Let $r_{\mu\lambda}$ denote the multiplicity of the irreducible representation $V_\mu$ of $S_n$, corresponding to a…

In a recent paper on a study of the Sylow 2-subgroups of the symmetric group with 2^n elements it has been show that the growth of the first (n-2) consecutive indices of a certain normalizer chain is linked to the sequence of partitions of…

In this notes we construct and count all ordinary irreducible characters of Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$.

Let $p$ be an odd prime and let $n$ be a natural number. In this article we determine the irreducible constituents of the permutation module induced by the action of the symmetric group $\mathfrak{S}_n$ on the cosets of a Sylow $p$-subgroup…

We show that the Sylow $p$-subgroups of a symmetric group, respectively an alternating group, are characterized as the $p$-subgroups containing all elementary abelian $p$-subgroups up to conjugacy of the symmetric group, respectively the…

Given an odd prime $p$, we identify composition factors of the reduction modulo $p$ of spin irreducible representations of the covering groups of symmetric groups indexed by partitions with 2 parts and find some decomposition numbers.

We use binary trees to study the Bratteli diagram of Sylow 2-subgroups of symmetric groups. We show that it is simple, has a recursive structure, and self-similarities at all scales. We contrast its subgraph of one-dimensional…

The covering number of a non-linear character $\chi$ of a finite group $G$ is the least positive integer $k$ such that every irreducible character of $G$ occurs in $\chi^k$. We determine the covering numbers of irreducible characters of the…

We study the irreducible components of special loci of curves whose group of symmetries is given as certain group extension. We introduce some relative Hurwitz data, which we show by using mixed \'etale cohomology theory, identifies some…

In this note, we formulate an observation that "almost all" irreducible ordinary characters of finite groups of Lie type remain irreducible when restricted to the derived subgroups. To see this, key ingredients are some asymptotic results…

Considered are eighty sets of layer groups, each set consisted of four groups: ordinary single and double, and gray single and double layer group. Structural properties of layer groups (factorization onto cyclic subgroups and existence of…