Intransitive Permutation Groups with Bounded Movement Having Maximum Degree

Let G be a permutation group on a set withno fixed points in and let m be a positive integer. If for each subset T of the size |Tg\T| is bounded, for gEG, we define the movement of g as the max|Tg\T| over all subsets T of . In this paper we classified all of permutation groups on set of size 3m + 1 with 2 orbits such that has movement m . 2000 AMS classification subjects: 20B25

Intransitive Permutation Groups with Bounded Movement Having Maximum Degree

Let G be a permutation group on a set with no fixed points in and let m be a positive integer. If for each subset of the size is bounded, for , we define the movement of g as the max over all subsets of . In this paper we classified all of permutation groups on set of size 3m + 1 with 2 orbits such that has movement m . 2000 AMS classification subjects: 20B25

Clause-Bounded Movement: Stylistic Fronting and Phase Theory

In this squib, we provide novel empirical support for treating the thematic domain—the vP—as a locality domain like CP (a phase), in agreement with a growing body of research (see Fox 1999 , Barbiers 2002 , Legate 2003 , Rackowski and Richards 2005 , Cozier 2006 , Kahnemuyipour and Megerdoomian 2011 , Buell 2012 , Van Urk and Richards 2015 ; see Den Dikken 2006 for an opposing view). We show how vP phasehood solves a previously unsolved problem for defining the locality of Icelandic Stylistic Fronting. We present novel data to show that Stylistic Fronting of verbs and particles can only cross one phase boundary, a generalization that is empirically superior to clause-boundedness. Our study supports the view that v defines a phase edge whether the verb is linked to an external argument or not ( Legate 2003 , Marantz 2007 ).

Improvement on the bounds of permutation groups with bounded movement

Let G be a permutation group on a set Ω with no fixed points in Ω and let m be a positive integer. Then we define the movement of G as, m := move(G) := supΓ{|Γg \ Γ| │ g ∈ G}. Let p be a prime, p ≥ 5. If G is not a 2-group and p is the least odd prime dividing |G|, then we show that n := |Ω| ≤ 4m – p + 3.Moreover, if we suppose that the permutation group induced by G on each orbit is not a 2-group then we improve the last bound of n and for an infinite family of groups the bound is attained.