Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The subclass algebra associated with a finite group and subgroup


Author: John Karlof
Journal: Trans. Amer. Math. Soc. 207 (1975), 329-341
MSC: Primary 20C05
MathSciNet review: 0367040
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a finite group and let $ H$ be a subgroup of $ G$. If $ g \in G$, then the set $ {E_g} = \{ hg{h^{ - 1}}\vert h \in H\} $ is the subclass of $ G$ containing $ g$ and $ {\Sigma _{x \in {E_g}}}x$ is the subclass sum containing $ g$. The algebra over the field of complex numbers generated by these subclass sums is called the subclass algebra (denoted by $ S$) associated with $ G$ and $ H$. The irreducible modules of $ S$ are demonstrated, and results about Schur algebras are used to develop formulas relating the irreducible characters of $ S$ to the irreducible characters of $ G$ and $ H$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20C05

Retrieve articles in all journals with MSC: 20C05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1975-0367040-2
PII: S 0002-9947(1975)0367040-2
Article copyright: © Copyright 1975 American Mathematical Society