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The field of Nash functions and factorization of polynomials

100%

Spodzieja S.

Annales Polonici Mathematici

1996-1997

tom 65

nr 1

81-94

The algebraically closed field of Nash functions is introduced. It is shown that this field is an algebraic closure of the field of rational functions in several variables. We give conditions for the irreducibility of polynomials with Nash coefficients, a description of factors of a polynomial over the field of Nash functions and a theorem on continuity of factors.

Periodic subgroups of projective linear groups in positive characteristic

88%

Detinko A., Flannery D.

Open Mathematics

2008

tom 6

nr 3

384-392

We classify the maximal irreducible periodic subgroups of PGL(q, $$ \mathbb{F} $$ ), where $$ \mathbb{F} $$ is a field of positive characteristic p transcendental over its prime subfield, q = p is prime, and $$ \mathbb{F} $$ × has an element of order q. That is, we construct a list of irreducible subgroups G of GL(q, $$ \mathbb{F} $$ ) containing the centre $$ \mathbb{F} $$ ×1q of GL(q, $$ \mathbb{F} $$ ), such that G/$$ \mathbb{F} $$ ×1q is a maximal periodic subgroup of PGL(q, $$ \mathbb{F} $$ ), and if H is another group of this kind then H is GL(q, $$ \mathbb{F} $$ )-conjugate to a group in the list. We give criteria for determining when two listed groups are conjugate, and show that a maximal irreducible periodic subgroup of PGL(q, $$ \mathbb{F} $$ ) is self-normalising.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Open Mathematics

1 Detinko A.

1 Flannery D.

1 Spodzieja S.

1 2008

1 1996

Wyniki wyszukiwania

The field of Nash functions and factorization of polynomials

Periodic subgroups of projective linear groups in positive characteristic