The Projective Cover of the Trivial Module Over a Group Algebra of a Finite Group

We determine all finite groups G such that the Loewy length (socle length) of the projective cover P(k G ) of the trivial kG-module k G is four, where k is a field of characteristic p > 0 and kG is the group algebra of G over k, by using previous results and also the classification of finite simp...

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Bibliographic Details
Published inCommunications in algebra Vol. 42; no. 10; pp. 4308 - 4321
Main Author Koshitani, Shigeo
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.01.2014
Subjects
Algebra
Blocking
Byproducts
Classification
Conjugacy class of involutions
Group theory
Loewy length
Mathematical analysis
Modules
Principal block
Projective cover
Socle length
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Summary:We determine all finite groups G such that the Loewy length (socle length) of the projective cover P(k G ) of the trivial kG-module k G is four, where k is a field of characteristic p > 0 and kG is the group algebra of G over k, by using previous results and also the classification of finite simple groups. As a by-product we prove also that if p = 2 then all finite groups G such that the Loewy lengths of the principal block algebras of kG are four, are determined.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2013.809532