## Abstract

Let F be a field of characteristic different from 2. It is shown that the problems of Classifying (i) local commutative associative algebras over F with zero cube radical, (ii) Lie algebras over F with central commutator subalgebra of dimension 3, and (iii) finite p-groups of exponent p with central commutator subgroup of order p^{3} are hopeless since each of them contains · the problem of classifying symmetric bilinear mappings U × U → V, or · the problem of classifying skew-symmetric bilinear mappings U × U → V, in which U and V are vector spaces over F (consisting of p elements for p-groups (iii)) and V is 3-dimensional. The latter two problems are hopeless since they are wild; i.e., each of them contains the problem of classifying pairs of matrices over F up to similarity.

Original language | English |
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Pages (from-to) | 516-529 |

Number of pages | 14 |

Journal | Electronic Journal of Linear Algebra |

Volume | 18 |

State | Published - 1 Jan 2009 |

## Keywords

- Associative algebras
- Classification
- Lie algebras
- Metabelian groups
- Wild problems

## ASJC Scopus subject areas

- Algebra and Number Theory