Groups of finite Morley rank with a generically multiply transitive action on an abelian group [PDF]
Model Theory, 2022 We investigate the configuration where a group of finite Morley rank acts definably and generically $m$-transitively on an elementary abelian $p$-group of Morley rank $n$, where $p$ is an odd prime, and $m\geqslant n$. We conclude that $m=n$, and the action is equivalent to the natural action of $\operatorname{GL}_n(F)$ on $F^n$ for some algebraically ...
Berkman, Ayşe, Borovik, Alexandre
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Groups of finite Morley rank with a generically sharply multiply transitive action [PDF]
Journal of Algebra, 2018 We prove that if $G$ is a group of finite Morley rank which acts definably and generically sharply $n$-transitively on a connected abelian group $V$ of Morley rank $n$ with no involutions, then there is an algebraically closed field $F$ of characteristic $\ne 2$ such that $V$ has a structure of a vector space of dimension $n$ over $F$ and $G$ acts on ...
Berkman, Ay��e, Borovik, Alexandre
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Normal subgroups of finite multiply transitive permutation groups [PDF]
Nagoya Mathematical Journal, 1974 Wagner [5] and Ito [2] proved the following theorems respectively.THEOREM OF WAGNER. Let G be a triply transitive permutation group on a set Ω = {1,2, …, n}, and let n be odd and n > 4. If H is a normal subgroup (≠1) of G, then H is also triply transitive on Ω.
Eiichi Bannaĭ
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Kinematic self-similar locally rotationally symmetric models [PDF]
, 1998 A brief summary of results on kinematic self-similarities in general relativity is given. Attention is focussed on locally rotationally symmetric models admitting kinematic self-similar vectors.
A M Sintes +21 more
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Hurwitz Monodromy and Full Number Fields [PDF]
, 2014 We give conditions for the monodromy group of a Hurwitz space over the configuration space of branch points to be the full alternating or symmetric group on the degree.
Roberts, David P., Venkatesh, Akshay
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Galois theory on the line in nonzero characteristic [PDF]
, 1992 The author surveys Galois theory of function fields with non-zero caracteristic and its relation to the structure of finite permutation groups and matrix groups.Comment: 66 pages.
Abhyankar, Shreeram S.
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Linear growth for semigroups which are disjoint unions of finitely many copies of the free monogenic semigroup [PDF]
, 2015 We show that every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) has linear growth.
Abughazalah, Nabilah, Etingof, Pavel
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Bounds on the diameter of Cayley graphs of the symmetric group [PDF]
, 2012 In this paper we are concerned with the conjecture that, for any set of generators S of the symmetric group of degree n, the word length in terms of S of every permutation is bounded above by a polynomial of n.
C.E. Praeger +23 more
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Graphs having no quantum symmetry [PDF]
, 2006 We consider circulant graphs having $p$ vertices, with $p$ prime. To any such graph we associate a certain number $k$, that we call type of the graph. We prove that for $p>>k$ the graph has no quantum symmetry, in the sense that the quantum automorphism ...
Banica, Teodor +2 more
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Two Generalizations of Homogeneity in Groups with Applications to Regular Semigroups [PDF]
, 2014 Let $X$ be a finite set such that $|X|=n$ and let $i\leq j \leq n$. A group $G\leq \sym$ is said to be $(i,j)$-homogeneous if for every $I,J\subseteq X$, such that $|I|=i$ and $|J|=j$, there exists $g\in G$ such that $Ig\subseteq J$.
Araújo, João, Cameron, Peter J.
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