Iwasawa group

In mathematics a group is sometimes called an Iwasawa group or M-group or modular group if its lattice of subgroups is modular.

Finite modular groups are also called Iwasawa groups, after harv|Iwasawa|1941 where they were classified. Both finite and infinite M-groups are presented in textbook form in harv|Schmidt|1994|loc=Ch. 2.4. Modern study includes harv|Zimmerman|1989. A finite "p"-group is a modular group if and only if every subgroup is permutable, by harv|Schmidt|1994|loc=Lemma 2.3.2, p. 55. Every subgroup of a finite "p"-group is subnormal, and those finite groups in which subnormality and permutability coincide are called PT-groups. In other words, a finite "p"-group is an Iwasawa group if and only if it is a PT-group.

References

Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать реферат

Look at other dictionaries:

Iwasawa — may refer to: *Kenkichi Iwasawa, mathematician **Iwasawa decomposition, a mathematical group decomposition **Iwasawa group, a mathematical group whose subgroup lattice is modular *Iwasawa manifold, a mathematical six dimensional space *Iwasawa… … Wikipedia
Iwasawa theory — In number theory, Iwasawa theory is the study of objects of arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa, in the 1950s, as part of the theory of … Wikipedia
Iwasawa decomposition — In mathematics, the Iwasawa decomposition KAN of a semisimple Lie group generalises the way a square real matrix can be written as a product of an orthogonal matrix and an upper triangular matrix (a consequence of Gram Schmidt orthogonalization) … Wikipedia
Iwasawa manifold — In mathematics, in the field of differential geometry, an Iwasawa manifold is a compact quotient of a 3 dimensional complex Heisenberg group by a cocompact, discrete subgroup. An Iwasawa manifold is a nilmanifold, of real dimension 6.As a complex … Wikipedia
Modular group — For a group whose lattice of subgroups is modular see Iwasawa group. In mathematics, the modular group Γ is a fundamental object of study in number theory, geometry, algebra, and many other areas of advanced mathematics. The modular group can be… … Wikipedia
M-group — In mathematics, especially in the field of group theory, the term M group may refer to a few distinct concepts: * monomial group, in character theory, a group whose complex irreducible characters are all monomial * Iwasawa group or modular group … Wikipedia
Kenkichi Iwasawa — (岩澤健吉 Iwasawa Kenkichi , September 11 1917 – October 26 1998) was a Japanese mathematician who is known for his influence on algebraic number theory.Iwasawa was born in Shinshuku mura, a town near Kiryu, in Gunma Prefecture. He attended… … Wikipedia
List of group theory topics — Contents 1 Structures and operations 2 Basic properties of groups 2.1 Group homomorphisms 3 Basic types of groups … Wikipedia
Covering group — This article is about topological covering group. For algebraic covering group, see universal perfect central extension. In mathematics, a covering group of a topological group H is a covering space G of H such that G is a topological group and… … Wikipedia
Weil–Châtelet group — In mathematics, particularly in arithmetic geometry, the Weil Châtelet group of an abelian variety A defined over a field K is the abelian group of principal homogeneous spaces for A , defined over K . It is named for André Weil, who introduced… … Wikipedia

Academic Dictionaries and Encyclopedias

Iwasawa group

Look at other dictionaries:

Share the article and excerpts

Academic Dictionaries and Encyclopedias

Wikipedia

Iwasawa group

Look at other dictionaries:

Share the article and excerpts

Direct link