Author
Susan Claire Dancs
Bio: Susan Claire Dancs is an academic researcher. The author has contributed to research in topics: Locally finite group & Abelian group. The author has an hindex of 1, co-authored 1 publications receiving 5 citations.
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TL;DR: In this article, the order of maximal abelian subgroups of central powers and crown products of finite p-groups is obtained, which is used to construct groups with "tsmall" maximal ABELIAN subgroups.
Abstract: Information is obtained about the order of maximal abelian subgroups of central powers and crown products of finite p-groups. This is used to construct groups with "tsmall" maximal abelian subgroups.
5 citations
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TL;DR: In this article, it was shown that the moduli of morphisms on Pn generalizes the study of rational maps on P1, and that the quotient space is rational for all d > 1.
Abstract: The theory of moduli of morphisms on Pn generalizes the study of rational maps on P1. This paper proves three results about the space of morphisms on Pn of degree d > 1, and its quotient by the conjugation action of PGL(n+1). First, we prove that this quotient is geometric, and compute the stable and semistable completions of the space of morphisms. This strengthens previous results of Silverman, as well as of Petsche, Szpiro, and Tepper. Second, we bound the size of the stabilizer group in PGL(n + 1) of every morphism in terms of only n and d. Third, we specialize to the case where n = 1, and show that the quotient space is rational for all d > 1; this partly generalizes a result of Silverman about the case d = 2.
58 citations
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TL;DR: The theory of moduli of morphisms on P^n generalizes the study of rational maps on p^1 as discussed by the authors, and it has been shown that the quotient space is rational for all degree d > 1 and that the stabilizer group in PGL(n+1) of every morphism in terms of only n and d is rational.
Abstract: The theory of moduli of morphisms on P^n generalizes the study of rational maps on P^1. This paper proves three results about the space of morphisms on P^n of degree d > 1, and its quotient by the conjugation action of PGL(n+1). First, we prove that this quotient is geometric, and compute the stable and semistable completions of the space of morphisms. This strengthens previous results of Silverman, as well as of Petsche, Szpiro, and Tepper. Second, we bound the size of the stabilizer group in PGL(n+1) of every morphism in terms of only n and d. Third, we specialize to the case where n = 1, and show that the quotient space is rational for all d > 1; this partly generalizes a result of Silverman about the case d = 2.
42 citations
TL;DR: In this paper, a subspace W is said to be isotropic for a skewform if the restriction of a to W is null, i.e., a(x, y) = 0 for all X, YE W.
19 citations
TL;DR: Brauer and Fowler as discussed by the authors showed that every non-abeliansolvable groupG contains an elementx∈G−Z such that|C G(x)|>|G|1/2.
Abstract: In 1955 R. Brauer and K. A. Fowler showed that ifG is a group of even order >2, and the order |Z(G)| of the center ofG is odd, then there exists a strongly real) elementx∈G−Z whose centralizer satisfies|C G(x)|>|G|1/3. In Theorem 1 we show that every non-abeliansolvable groupG contains an elementx∈G−Z such that|C G(x)|>[G:G′∩Z]1/2 (and thus|C G(x)|>|G|1/3). We also note that if non-abelianG is either metabelian, nilpotent or (more generally) supersolvable, or anA-group, or any Frobenius group, then|C G(x)|>|G|1/2 for somex∈G−Z. In Theorem 2 we prove that every non-abelian groupG of orderp mqn (p, q primes) contains a proper centralizer of order >|G|1/2. Finally, in Theorem 3 we show that theaverage |C(x)|, x∈G, is ≧c|G| 1/3 for metabelian groups, wherec is constant and the exponent 1/3 is best possible.
10 citations
DOI•
01 Jan 2011
TL;DR: Moduli Spaces of Dynamical Systems on P (MDS on P) as discussed by the authors ) is an extension of the Moduli Spaces for Dynamical systems (MSDS) model.
Abstract: Moduli Spaces of Dynamical Systems on P
1 citations