### Abstract

Original language | English |
---|---|

Pages (from-to) | 288-299 |

Number of pages | 12 |

Journal | Journal of Algebra |

Volume | 414 |

Early online date | 16 Jun 2014 |

DOIs | |

Publication status | Published - 15 Sep 2014 |

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### Keywords

- modular representations
- elementary abelian groups
- Loewy length

### Cite this

*Journal of Algebra*,

*414*, 288-299. https://doi.org/10.1016/j.jalgebra.2014.05.028

**Modules with small Loewy length.** / Benson, David; Reid, Fergus.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 414, pp. 288-299. https://doi.org/10.1016/j.jalgebra.2014.05.028

}

TY - JOUR

T1 - Modules with small Loewy length

AU - Benson, David

AU - Reid, Fergus

PY - 2014/9/15

Y1 - 2014/9/15

N2 - A module of complexity c for E≅(Z/p)r in characteristic p has Loewy length at least (p−1)(r−c)+1. We study the case of equality. If p is odd, the only rank varieties possible are finite unions of linear subspaces of dimension c , and every such rank variety occurs. If p=2, the variety has to be equidimensional. If such a variety is a finite union of set theoretic complete intersections then it occurs for such a module, but otherwise the situation is unclear. Exterior algebras in any characteristic are also treated, and follow the same behaviour as the case p=2 above.

AB - A module of complexity c for E≅(Z/p)r in characteristic p has Loewy length at least (p−1)(r−c)+1. We study the case of equality. If p is odd, the only rank varieties possible are finite unions of linear subspaces of dimension c , and every such rank variety occurs. If p=2, the variety has to be equidimensional. If such a variety is a finite union of set theoretic complete intersections then it occurs for such a module, but otherwise the situation is unclear. Exterior algebras in any characteristic are also treated, and follow the same behaviour as the case p=2 above.

KW - modular representations

KW - elementary abelian groups

KW - Loewy length

U2 - 10.1016/j.jalgebra.2014.05.028

DO - 10.1016/j.jalgebra.2014.05.028

M3 - Article

VL - 414

SP - 288

EP - 299

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -