TY - JOUR

T1 - Fusions of character tables and Schur rings of abelian groups

AU - Humphries, Stephen P.

AU - Johnson, Kenneth

PY - 2008/4/1

Y1 - 2008/4/1

N2 - If the character table of a finite group H satisfies certain conditions, then the classes and characters of H can fuse to give the character table of a group G of the same order. We investigate the case where H is an abelian group. The theory is developed in terms of the S-rings of Schur and Wielandt. We discuss certain classes of p-groups which fuse from abelian groups and give examples of such groups which do not. We also show that a large class of simple groups do not fuse from abelian groups. The methods to show fusion include the use of extensions which are Camina pairs, but other techniques on S-rings are also developed.

AB - If the character table of a finite group H satisfies certain conditions, then the classes and characters of H can fuse to give the character table of a group G of the same order. We investigate the case where H is an abelian group. The theory is developed in terms of the S-rings of Schur and Wielandt. We discuss certain classes of p-groups which fuse from abelian groups and give examples of such groups which do not. We also show that a large class of simple groups do not fuse from abelian groups. The methods to show fusion include the use of extensions which are Camina pairs, but other techniques on S-rings are also developed.

UR - http://www.scopus.com/inward/record.url?scp=45949083667&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=45949083667&partnerID=8YFLogxK

U2 - 10.1080/00927870701866689

DO - 10.1080/00927870701866689

M3 - Article

AN - SCOPUS:45949083667

SN - 0092-7872

VL - 36

SP - 1437

EP - 1460

JO - Communications in Algebra

JF - Communications in Algebra

IS - 4

ER -