Fusions of Character Tables and Schur Rings of Abelian Groups |
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Authors: | Stephen P Humphries Kenneth W Johnson |
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Institution: | 1. Department of Mathematics , Brigham Young University , Provo, Utah, USA steve@math.byu.edu;3. Department of Mathematics , Pennsylvania State University , Ogontz Campus Abington, Pennsylvania, USA |
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Abstract: | 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. |
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Keywords: | Quasi p-injective module Self generator Annihilator 1991 Mathematics Subject Classification: 16D50 16D70 16D80 |
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