On the almost split sequences for relatively projective modules over a finite group

Author:
Mark Kleiner

Journal:
Proc. Amer. Math. Soc. **116** (1992), 943-947

MSC:
Primary 16G70

DOI:
https://doi.org/10.1090/S0002-9939-1992-1100656-X

MathSciNet review:
1100656

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Abstract: Let be a finite group with a subgroup . Given a field of characteristic dividing the order of , denote by the category of finite-dimensional over left -modules, and let be the full subcategory of determined by the relatively projective modules. Let be an exact sequence in with . It is proved that the sequence is an almost split sequence in if and only if it is an almost split sequence in . This implies, together with a recent result of Carlson and Happel, that has almost split sequences if and only if it is closed under extensions, i.e., if and only if is coprime to either the order of or the index of in .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1992-1100656-X

Keywords:
Almost split sequence,
relatively projective module,
finite group

Article copyright:
© Copyright 1992
American Mathematical Society