Related papers: Quasi-reductive supergroups with small even parts

We introduce the notion of a quasi-connected reductive group over an arbitrary field to be an almost direct product of a connected semisimple group and a quasi-torus (a smooth group of multiplicative type). We show that a linear algebraic…

We call an affine algebraic supergroup quasireductive if its underlying algebraic group is reductive. We obtain some results about the structure and representations of reductive supergroups.

We determine all maximal subgroups of the almost simple groups with socle $T=\PSL(2,q)$, that is, of all groups $G$ such that $\PSL(2,q)\leqslant G\leqslant\PGammaL(2,q)$, with $q\geq 4$.

We investigate the class of quasitrivial semigroups and provide various characterizations of the subclass of quasitrivial and commutative semigroups as well as the subclass of quasitrivial and order-preserving semigroups. We also determine…

By a quasi-connected reductive group (a term of Labesse) over an arbitrary field we mean an almost direct product of a connected semisimple group and a quasi-torus (a smooth group of multiplicative type). We show that a linear algebraic…

A semisimple element $s$ of a connected reductive group $G$ is said {\it quasi-isolated} (respectively {\it isolated}) if $C_G(s)$ (respectively $C_G^0(s)$) is not contained in a Levi subgroup of a proper parabolic subgroup of $G$. We study…

Sela introduced limit groups in his work on the Tarski problem, and showed that each limit group has a cyclic hierarchy. In this paper, a class of relatively hyperbolic groups, equipped with a hierarchy similar to the one for limit groups,…

A connected algebraic group Q defined over a field of characteristic zero is quasi-reductive if there is an element of its dual of reductive type, that is such that the quotient of its stabiliser by the centre of Q is a reductive subgroup…

We introduce the notion of splitting subgroups of quasireducitve supergroups, and explain their significance. For $GL(m|n)$, $Q(n)$, and defect one basic classical supergroups, we give explicit splitting subgroups. We further prove they are…

We incorporate covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. We work with all covers that arise from extensions of quasisplit reductive groups by $\mathbf{K}_2$ -- the…

We classify closed abelian subgroups of the simple groups $G_2$, $F_4$, $Aut(so(8))$ having centralizer the same dimension as the dimension of the subgroup, as well as finite abelian subgroups of certain spin and half-spin groups having…

We determine subnormalisers of semisimple elements of prime power order in finite quasi-simple groups of Lie type. For this, we determine the maximal overgroups of normalisers of Sylow tori. This is motivated by the recent character…

We classify up to equivalence all finite-dimensional irreducible representations of PSL2(Z) whose restriction to the commutator subgroup is diagonalizable.

We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups,…

The representation category $\mathcal{A} = Rep(G,\epsilon)$ of a supergroup scheme $G$ has a largest proper tensor ideal, the ideal $\mathcal{N}$ of negligible morphisms. If we divide $\mathcal{A}$ by $\mathcal{N}$ we get the semisimple…

In this paper, we consider semi-extraspecial $p$-groups $G$ that have an automorphism of order $|G:G'| - 1$. We prove that these groups are isomorphic to Sylow $p$-subgroups of ${\rm SU}_3 (p^{2a})$ for some integer $a$. If $p$ is odd, this…

We enumerate the number of isoclinism classes of semi-extraspecial $p$-groups with derived subgroup of order $p^2$. To do this, we enumerate $\text{GL}(2, p)$-orbits of sets of irreducible, monic polynomials in $\mathbb{F}_p[x]$. Along the…

In this paper, we study almost subnormal subgroups of the general linear group $\GL_n(D)$ of degree $n\ge 1$ over a division ring $D$ that satisfy a generalized power central group identity.

This paper determines almost symmetric numerical semigroups with maximal reduced type completely. In addition, this paper classifies MED-semigroups with maximal reduced type.

Let $p$ be a prime. A $p$-group $G$ is defined to be semi-extraspecial if for every maximal subgroup $N$ in $Z(G)$ the quotient $G/N$ is a an extraspecial group. In addition, we say that $G$ is ultraspecial if $G$ is semi-extraspecial and…