Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On double centralizer subgroups of some finite $ p$-groups


Author: Ying Cheng
Journal: Proc. Amer. Math. Soc. 86 (1982), 205-208
MSC: Primary 20D15
DOI: https://doi.org/10.1090/S0002-9939-1982-0667273-0
MathSciNet review: 667273
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ A$ be a maximal abelian normal subgroup of a finite $ p$-group $ G(p > 2)$ such that $ [G,A]$ is cyclic. Then (i) $ {C_G}({C_G}(D)) = D$ and $ [G:{C_G}(D)] = [D:Z(G)]$ for every $ Z(G) \leqslant D \leqslant G$; (ii) $ [G:Z(G)] = {[G,A]^2}$ and every faithful absolutely irreducible representation of $ G$ is of degree $ [G:A]$. The case $ p = 2$ will also be mentioned.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20D15

Retrieve articles in all journals with MSC: 20D15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0667273-0
Keywords: Commutator subgroup, Azumaya algebras
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society