Topic
Subgroup
About: Subgroup is a research topic. Over the lifetime, 2013 publications have been published within this topic receiving 20689 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this paper, the homological properties of the factor space G/P, where G is a complex semisimple Lie group and P a parabolic subgroup of G, were studied.
Abstract: We study the homological properties of the factor space G/P, where G is a complex semisimple Lie group and P a parabolic subgroup of G To this end we compare two descriptions of the cohomology of such spaces One of these makes use of the partition of G/P into cells (Schubert cells), while the other consists in identifying the cohomology of G/P with certain polynomials on the Lie algebra of the Cartan subgroup H of G The results obtained are used to describe the algebraic action of the Weyl group W of G on the cohomology of G/P
469 citations
TL;DR: In this paper, it was shown that if G and H are two non-abelian finite groups such that Γ G ≅ Γ H, then | G | = | H |, then H is nilpotent.
374 citations
TL;DR: The notion of coverings of tree actions was introduced in this article, which is a useful tool for producing subgroups of a tree action with prescribed properties and yields a strong Conjugacy Theorem for groups acting freely on a tree X.
361 citations
TL;DR: Theorem 1.1.1 as discussed by the authors shows that a semisimple Lie group with finite center has a discrete series if rank (G) = rank (K), where K is a maximal compact subgroup.
Abstract: We give a sufficient condition for the existence of minimal closed G-invariant subspaces of L2(G/H) for a semisimple symmetric space G/H. As a semisimple Lie group with finite center may always be considered as a symmetric space, this provides, in particular, a new and elementary proof of Harish-Chandra's result that G has a discrete series if rank (G) = rank (K), where K is a maximal compact subgroup. Let G be a connected noncompact semisimple Lie group, let z be an involution on G, and let H be the connected component of the fixed-point group Gr containing the identity. Then G/H is a semisimple symmetric space, and the group G acts by left translation on C*(G/H) and L2(G/H). In the introduction we will, for simplicity, assume that G has a finite center. By the discrete series for G/H we shall mean the set of equivalence classes of the representations of G on minimal closed invariant subspaces of L2(G/H). Let a be a Cartan involution commuting with z. The fixed-point group K for a is a maximal compact subgroup. Our main result is THEOREM 1.1. The discrete series for G/H is nonempty and infinite if
247 citations
TL;DR: In this article, it was shown that every quasiconvex subgroup of a word-hyperbolic group is a virtual retract, and hence separable from the group.
Abstract: Let $G$ be a word-hyperbolic group with a quasiconvex hierarchy.
We show that $G$ has a finite index subgroup $G'$ that embeds as a
quasiconvex subgroup of a right-angled Artin group.
It follows that every quasiconvex subgroup of $G$ is a virtual retract,
and is hence separable.
The results are applied to certain 3-manifold and one-relator groups.
203 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2024 | 3 |
| 2023 | 16 |
| 2022 | 24 |
| 2021 | 13 |
| 2020 | 17 |
| 2019 | 15 |