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On a conjecture of V. V. Shchigolev | C. Bekh-Ochir
; S. A. Rankin
; | Date: |
9 Nov 2009 | Abstract: | V. V. Shchigolev has proven that over any infinite field k of characteristic
p>2, the T-space generated by G={x_1^p,x_1^px_2^p,...} is finitely based, which
answered a question raised by A. V. Grishin. Shchigolev went on to conjecture
that every infinite subset of G generated a finitely based T-space. In this
paper, we prove that Shchigolev’s conjecture was correct by showing that for
any field of characteristic p>2, the T-space generated by any subset
{x_1^px_2^p...x_{i_1}^p, x_1^px_2^p...x_{i_2}^p,...}, i_1<i_2<i_3<..., of G has
a T-space basis of size at most i_2-i_1+1. | Source: | arXiv, 0911.1709 | Services: | Forum | Review | PDF | Favorites |
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