T-group (mathematics)

T-group (mathematics)

In mathematics, in the field of group theory, a T-group is a group in which the property of normality is transitive, that is, every subnormal subgroup is normal. Here are some facts about T-groups:

*Every abelian group and every Hamiltonian group is a T-group.
*Every nilpotent T-group is either abelian or Hamiltonian, because in a nilpotent group, every subgroup is subnormal.
*Every normal subgroup of a T-group is a T-group.
*Every solvable T-group is metabelian.


Wikimedia Foundation. 2010.

Игры ⚽ Поможем сделать НИР

Look at other dictionaries:

  • Group (mathematics) — This article covers basic notions. For advanced topics, see Group theory. The possible manipulations of this Rubik s Cube form a group. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines …   Wikipedia

  • McLaughlin group (mathematics) — For the television program, see The McLaughlin Group. In the mathematical discipline known as group theory, the McLaughlin group McL is a sporadic simple group of order 27 · 36 · 53· 7 · 11 = 898,128,000, discovered by McLaughlin (1969) as an… …   Wikipedia

  • Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia

  • Group — can refer to: Sociology * Group action (sociology) * Group behaviour * Groups of people, a description of various different human groups ** Peer group ** Workgroup * Group dynamics * Group (sociology), a sub set of a culture or of a society *… …   Wikipedia

  • Mathematics, Form and Function — is a survey of the whole of mathematics, including its origins and deep structure, by the American mathematician Saunders Mac Lane. Contents 1 Mac Lane s relevance to the philosophy of mathematics 2 Mathematics and human activities …   Wikipedia

  • Mathematics (producer) — Mathematics At the Eurockéennes of 2007. Background information Also known as Allah Mathematics Origin …   Wikipedia

  • Mathematics and art — have a long historical relationship. The ancient Egyptians and ancient Greeks knew about the golden ratio, regarded as an aesthetically pleasing ratio, and incorporated it into the design of monuments including the Great Pyramid,[1] the Parthenon …   Wikipedia

  • Mathematics Mechanization and Automated Reasoning Platform — Original author(s) 中国科学院数学机械化重点实验室 Developer(s) 中國 国家基础研究发展规划项目 数学机械化与自动推理平台 软件开发课题组 Stable release 3.0 / April 1, 2006; 5 years ago (2006 04 01) …   Wikipedia

  • Group decision making — (also known as collaborative decision making) is a situation faced when individuals are brought together in a group to solve problems. According to the idea of synergy, decisions made collectively tend to be more effective than decisions made by… …   Wikipedia

  • mathematics — [math΄ə mat′iks] n. [see MATHEMATICAL & ICS] 1. the group of sciences (including arithmetic, geometry, algebra, calculus, etc.) dealing with quantities, magnitudes, and forms, and their relationships, attributes, etc., by the use of numbers and… …   English World dictionary

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”