(1) Andrei Pavelescu, “Derangements in Cosets of Primitive Permutation Groups”

PUBLICATION LIST
ANDREI PAVELESCU
(1) Andrei Pavelescu, “Derangements in Cosets of Primitive Permutation Groups”
J. Group Theory, Ahead of Print DOI 10.1515/jgth-2014-0030
http://arxiv.org/abs/1312.1422
Abstract. Let A be a primitive permutation group and G a normal subgroup of A such that A/G is cyclic. Let a be a generator for A/G. Motivated
by questions arising in connection to coverings of smooth connected projective curves, we study the proportion of derangements in the coset aG. We
use the Aschbacher-O’Nan-Scott theorem for primitive groups to partition the
problem and provide answers in the affine case and regular nonabelian normal subgroup case. We further study the applications to coverings of smooth
connected projective curves.
(2) Andrei Pavelescu,“Some Maximal Commutative Subrings of Mn (D)”
Communications in Algebra Vol. 41, Iss. 8, 2013
Abstract. We answer a question of Charles Weibel and prove that maximal
commutative subrings of simple Artinian rings are finite products of zero dimensional local rings. If the rings are reduced, we prove they are Artinian.
If they contain nilpotent elements, we give examples where the rings are and
are not Artinian.
(3) A. Pavelescu, “The Henselization of General Local Rings -Revisited-”-M.Phil.
Thesis, advisor Florian Pop, Published by University of Pennsylvania
Abstract. We revisit the notion of “Henselization” as a direct limit over a
specific filtrant subcategory of local algebras. We then connect this notion
with the better known definitions of a Hensel ring and prove that our construction is the Henselian closure. We provide examples naturally arising in
algebraic geometry.
Oklahoma State University, Stillwater, OK
E-mail address: andrei.pavelescu@okstate.edu
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