Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Publication

Counting conjugacy classes of cyclic subgroups for fusion systems

Sejong Park
2014
Journal Articles

Abstract

Thévenaz [6] made an interesting observation that the number of conjugacy classes of cyclic subgroups in a finite group G is equal to the rank of the matrix of the numbers of double cosets in G. We give another proof of this fact and present a fusion system version of it. In particular we use finite groups realizing the fusion system F as in our previous work [3].

Official source

Sejong Park
2014
Journal Articles

Abstract

Official source

Ontological neighbourhood

Mathematics

Algebra: Representation theory

Related concepts (32)

Finite group

In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving transformations. Important examples of finite groups include cyclic groups and permutation groups. The study of finite groups has been an integral part of group theory since it arose in the 19th century.

Representation theory of finite groups

The representation theory of groups is a part of mathematics which examines how groups act on given structures. Here the focus is in particular on operations of groups on vector spaces. Nevertheless, groups acting on other groups or on sets are also considered. For more details, please refer to the section on permutation representations. Other than a few marked exceptions, only finite groups will be considered in this article. We will also restrict ourselves to vector spaces over fields of characteristic zero.

Fusion power

Fusion power is a proposed form of power generation that would generate electricity by using heat from nuclear fusion reactions. In a fusion process, two lighter atomic nuclei combine to form a heavier nucleus, while releasing energy. Devices designed to harness this energy are known as fusion reactors. Research into fusion reactors began in the 1940s, but as of 2023, no device has reached net power. Fusion processes require fuel and a confined environment with sufficient temperature, pressure, and confinement time to create a plasma in which fusion can occur.

Related publications (32)

Counting conjugacy classes of cyclic subgroups for fusion systems

Graph Chatbot

Global fluid simulations of plasma turbulence in stellarators

Nonlinear simulation of plasma turbulence using a gyrokinetic moment-based approach

Models implemented in the methodological approach to design the initial STEP first wall contour