A completion procedure for computing canonical basis for a k-Subalgebra
Proceedings of the third conference on Computers and mathematics
Computing bases for rings of permutation-invariant polynomials
Journal of Symbolic Computation
Analogs of Gro¨bner bases in polynomial rings over a ring
Journal of Symbolic Computation
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
A constructive description of SAGBI bases for polynomial invariants of permutations groups
Journal of Symbolic Computation
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Let V be a finite dimensional representation of a p-group, G, over a field, k, of characteristic p. We show that there exists a choice of basis and monomial order for which the ring of invariants, k[V]G, has a finite SAGBI basis. We describe two algorithms for constructing a generating set for k[V]G. We use these methods to analyse k[2V3]U3 where U3 is the p-Sylow subgroup of GL3(Fp) and 2V3 is the sum of two copies of the canonical representation. We give a generating set for k[2V3]U3 for p = 3 and prove that the invariants fail to be Cohen-Macaulay for p 2. We also give a minimal generating set for k[mV2]Z/p were V2 is the two-dimensional indecomposable representation of the cyclic group Z/p.