#### Vol. 5, No. 1, 2011

 Recent Issues
 The Journal About the Journal Editorial Board Editors’ Interests Subscriptions Submission Guidelines Submission Form Policies for Authors Ethics Statement ISSN: 1944-7833 (e-only) ISSN: 1937-0652 (print) Author Index To Appear Other MSP Journals
Group algebra extensions of depth one

### Robert Boltje and Burkhard Külshammer

Vol. 5 (2011), No. 1, 63–73
##### Abstract

A ring extension $A\subseteq B$ is said to have depth one if $B$ is isomorphic to a direct summand of ${A}^{n}$ as an $\left(A,A\right)$-bimodule, for some positive integer $n$. We prove group-theoretic characterizations of this property in the case $kH\subseteq kG$, where $H$ is a subgroup of a finite group $G$ and $k$ is a field. We determine when the source algebra of a block of $kG$ with defect group $P$ is a depth-one extension of $kP$.

##### Keywords
depth-one ring extension, centrally projective ring extension, depth-two ring extension, symmetric Frobenius extension, $p$-hypoelementary group, nilpotent block, source algebra, trivial source module
##### Mathematical Subject Classification 2000
Primary: 20C05
Secondary: 19A22, 16D90, 16D20, 20C20