Essential subgroup

Essential subgroup

In mathematics, especially in the area of algebra studying the theory of abelian groups, an essential subgroup is a subgroup that determines much of the structure of its containing group. The concept was generalized to essential submodules.

Definition

A subgroup S of a (typically abelian) group G is said to be essential if whenever "H" is a non-trivial subgroup of "G", the intersection of "S" and "H" is non-trivial: here "non-trivial" means "containing an element other than the identity".

References

*


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Maximal compact subgroup — In mathematics, a maximal compact subgroup K of a topological group G is a subgroup K that is a compact space, in the subspace topology, and maximal amongst such subgroups. Maximal compact subgroups play an important role in the classification of …   Wikipedia

  • Divisible group — In mathematics, especially in the field of group theory, a divisible group is an abelian group in which every element can, in some sense, be divided by positive integers, or more accurately, every element is an nth multiple for each positive… …   Wikipedia

  • List of mathematics articles (E) — NOTOC E E₇ E (mathematical constant) E function E₈ lattice E₈ manifold E∞ operad E7½ E8 investigation tool Earley parser Early stopping Earnshaw s theorem Earth mover s distance East Journal on Approximations Eastern Arabic numerals Easton s… …   Wikipedia

  • Stallings theorem about ends of groups — In the mathematical subject of group theory, the Stallings theorem about ends of groups states that a finitely generated group G has more than one end if and only if the group G admits a nontrivial decomposition as an amalgamated free product or… …   Wikipedia

  • Character theory — This article refers to the use of the term character theory in mathematics. For the media studies definition, see Character theory (Media). In mathematics, more specifically in group theory, the character of a group representation is a function… …   Wikipedia

  • 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

  • Symmetric group — Not to be confused with Symmetry group. A Cayley graph of the symmetric group S4 …   Wikipedia

  • Control chart — One of the Seven Basic Tools of Quality First described by Walter A. Shewhart …   Wikipedia

  • Toll-like receptor — Toll like receptors (TLRs) are a class of single membrane spanning non catalytic receptors that recognize structurally conserved molecules derived from microbes once they have breached physical barriers such as the skin or intestinal tract mucosa …   Wikipedia

  • Systolic geometry — In mathematics, systolic geometry is the study of systolic invariants of manifolds and polyhedra, as initially conceived by Charles Loewner, and developed by Mikhail Gromov and others, in its arithmetic, ergodic, and topological manifestations.… …   Wikipedia

Share the article and excerpts

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