✦ LIBER ✦

Primitivity of Permutation Groups, Coherent Algebras and Matrices

✍ Scribed by Gareth A. Jones; Mikhail Klin; Yossi Moshe

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 114 KB
Volume: 98
Category: Article
ISSN: 0097-3165
DOI: 10.1006/jcta.2001.3245

No coin nor oath required. For personal study only.

✦ Synopsis

A coherent algebra is F-primitive if each of its non-identity basis matrices is primitive in the sense of Frobenius. We investigate the relationship between the primitivity of a permutation group, the primitivity of its centralizer algebra, and F-primitivity. The results obtained are applied to give new proofs of primitivity criteria for the exponentiations of permutation groups and of coherent algebras.

📜 SIMILAR VOLUMES

Factorizations of Primitive Permutation

Factorizations of Primitive Permutation Groups

✍ Barbara Baumeister 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 309 KB

Transitive Subgroups of Primitive Permut

Transitive Subgroups of Primitive Permutation Groups

✍ Martin W. Liebeck; Cheryl E. Praeger; Jan Saxl 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 492 KB

to helmut wielandt on the occasion of his 90th birthday We investigate the finite primitive permutation groups G which have a transitive subgroup containing no nontrivial subnormal subgroup of G. The conclusion is that such primitive groups are rather rare, and that their existence is intimately co

Asymptotic Results for Primitive Permuta

Asymptotic Results for Primitive Permutation Groups and Irreducible Linear Groups

✍ A. Lucchini; F. Menegazzo; M. Morigi 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 135 KB

A well-developed branch of asymptotic group theory studies the properties of classes of linear and permutation groups as functions of their degree. We refer to the surveys of Cameron [4] and Pyber [17,18] and the recent paper by Pyber and Shalev [19] for a detailed exposition of this subject. In thi

Incidence Matrices, Permutation Characte

Incidence Matrices, Permutation Characters, and the Minimal Genus of a Permutation Group

✍ Daniel Frohardt; Robert Guralnick; Kay Magaard 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 146 KB

Bases for Primitive Permutation Groups a

Bases for Primitive Permutation Groups and a Conjecture of Babai

✍ David Gluck; Ákos Seress; Aner Shalev 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 171 KB

A base of a permutation group G is a sequence B of points from the permutation domain such that only the identity of G fixes B pointwise. We show that primitive permutation groups with no alternating composition factors of degree greater than d and no classical composition factors of rank greater th

On the Minimal Degree of a Primitive Per

On the Minimal Degree of a Primitive Permutation Group

✍ Robert Guralnick; Kay Magaard 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 237 KB

We improve a result of Liebeck and Saxl concerning the minimal degree of a primitive permutation group and use it to strengthen a result of Guralnick and Neubauer on generic covers of Riemann surfaces.