scholarly journals Line-transitive Automorphism Groups of Linear Spaces

10.37236/1227 ◽  
1995 ◽  
Vol 3 (1) ◽  
Author(s):  
Alan R Camina ◽  
Susanne Mischke
Keyword(s):  
Automorphism Group ◽  
Projective Plane ◽  
Linear Space ◽  
Automorphism Groups ◽  
Linear Spaces ◽  
Full Automorphism Group ◽  
Transitive Automorphism

In this paper we prove the following theorem. Let $\cal S$ be a linear space. Assume that $\cal S$ has an automorphism group $G$ which is line-transitive and point-imprimitive with $k < 9$. Then $\cal S$ is one of the following:- (a) A projective plane of order $4$ or $7$, (b) One of $2$ linear spaces with $v=91$ and $k=6$, (c) One of $467$ linear spaces with $v=729$ and $k=8$. In all cases the full automorphism group Aut(${\cal S} \!$) is known.

Line-transitive point-imprimitive linear spaces with number of points being a product of two primes

2017 ◽  
Vol 16 (06) ◽  
pp. 1750110
Author(s):  
Haiyan Guan ◽  
Shenglin Zhou
Keyword(s):  
Linear Space ◽  
Automorphism Groups ◽  
Linear Spaces ◽  
Finite Linear Space ◽  
Transitive Point ◽  
Finite Linear

The work studies the line-transitive point-imprimitive automorphism groups of finite linear spaces, and is underway on the situation when the numbers of points are products of two primes. Let [Formula: see text] be a non-trivial finite linear space with [Formula: see text] points, where [Formula: see text] and [Formula: see text] are two primes. We prove that if [Formula: see text] is line-transitive point-imprimitive, then [Formula: see text] is solvable.

scholarly journals A 2-arc Transitive Hexavalent Nonnormal Cayley Graph on A119

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2935
Author(s):  
Bo Ling ◽  
Wanting Li ◽  
Bengong Lou
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Automorphism Groups ◽  
Cayley Graphs ◽  
Vital Role ◽  
Alternating Group ◽  
Full Automorphism Group ◽  
Base Group

A Cayley graph Γ=Cay(G,S) is said to be normal if the base group G is normal in AutΓ. The concept of the normality of Cayley graphs was first proposed by M.Y. Xu in 1998 and it plays a vital role in determining the full automorphism groups of Cayley graphs. In this paper, we construct an example of a 2-arc transitive hexavalent nonnormal Cayley graph on the alternating group A119. Furthermore, we determine the full automorphism group of this graph and show that it is isomorphic to A120.

Jordan property and automorphism groups of normal compact Kähler varieties

2018 ◽  
Vol 20 (03) ◽  
pp. 1750024 ◽  
Author(s):  
Jin Hong Kim
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Projective Varieties ◽  
Full Automorphism Group ◽  
Identity Component ◽  
Arbitrary Dimensions ◽  
Type Decomposition

It has been recently shown by Meng and Zhang that the full automorphism group [Formula: see text] is a Jordan group for all projective varieties in arbitrary dimensions. The aim of this paper is to show that the full automorphism group [Formula: see text] is, in fact, a Jordan group even for all normal compact Kähler varieties in arbitrary dimensions. The meromorphic structure of the identity component of the automorphism group and its Rosenlicht-type decomposition play crucial roles in the proof.

scholarly journals Automorphism groups of Cayley digraphs of ${\Bbb Z}_p^3$

10.37236/238 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Edward Dobson ◽  
István Kovács
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Full Automorphism Group ◽  
Product Action

We calculate the full automorphism group of Cayley digraphs of ${\Bbb Z}_p^3$, $p$ an odd prime, as well as determine the $2$-closed subgroups of $S_m \wr S_p$ with the product action.

scholarly journals Equality of certain automorphism groups of finite p-groups

2016 ◽  
Vol 15 (03) ◽  
pp. 1650056
Author(s):  
Deepak Gumber ◽  
Hemant Kalra
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Recent Past ◽  
Full Automorphism Group ◽  
Technical Lemma ◽  
Necessary And Sufficient

Let [Formula: see text] be a finite [Formula: see text]-group and let Aut([Formula: see text]) denote the full automorphism group of [Formula: see text]. In the recent past, there has been interest in finding necessary and sufficient conditions on [Formula: see text] such that certain subgroups of Aut([Formula: see text]) are equal. We prove a technical lemma and, as a consequence, obtain some new results and short and alternate proofs of some known results of this type.

Line-Transitive Automorphism Groups of Linear Spaces

1993 ◽  
Vol 25 (4) ◽  
pp. 309-315 ◽  
Author(s):  
Alan R. Camina ◽  
Cheryl E. Praeger
Keyword(s):  
Automorphism Groups ◽  
Linear Spaces ◽  
Transitive Automorphism

scholarly journals Latin squares with highly transitive automorphism groups

1982 ◽  
Vol 33 (1) ◽  
pp. 18-22 ◽  
Author(s):  
R. A. Bailey
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Latin Square ◽  
Latin Squares ◽  
Transitive Automorphism ◽  
Block System ◽  
Composition Table

AbstractA Latin square is considered to be a set of n2 cells with three block systems. An automorphisni is a permutation of the cells which preserves each block system. The automorphism group of a Latin Square necessarily has at least 4 orbits on unordered pairs of cells if n < 2. It is shown that there are exactly 4 orbits if and only if the square is the composition table of an elementary abelian 2-group or the cclic group of order 3.

Symmetric designs admitting flag-transitive and point-primitive almost simple automorphism groups of Lie type

2017 ◽  
Vol 16 (10) ◽  
pp. 1750192
Author(s):  
Yajie Wang ◽  
Shenglin Zhou
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Symmetric Design ◽  
Symmetric Designs ◽  
Full Automorphism Group ◽  
Design Formula ◽  
Groups Of Lie Type

Let [Formula: see text] be a subgroup of the full automorphism group of a [Formula: see text]-[Formula: see text] symmetric design [Formula: see text]. If [Formula: see text] is flag-transitive and point-primitive, then Soc[Formula: see text] cannot be [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].

scholarly journals On plane curves given by separated polynomials and their automorphisms

2020 ◽  
Vol 20 (1) ◽  
pp. 61-70
Author(s):  
Matteo Bonini ◽  
Maria Montanucci ◽  
Giovanni Zini
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Algebraic Closure ◽  
Sufficient Conditions ◽  
Plane Curve ◽  
Plane Curves ◽  
Prime Field ◽  
Full Automorphism Group ◽  
Ag Codes ◽  
Finite Prime Field

AbstractLet 𝓒 be a plane curve defined over the algebraic closure K of a finite prime field 𝔽p by a separated polynomial, that is 𝓒 : A(Y) = B(X), where A(Y) is an additive polynomial of degree pn and the degree m of B(X) is coprime with p. Plane curves given by separated polynomials are widely studied; however, their automorphism groups are not completely determined. In this paper we compute the full automorphism group of 𝓒 when m ≢ 1 mod pn and B(X) = Xm. Moreover, some sufficient conditions for the automorphism group of 𝓒 to imply that B(X) = Xm are provided. Also, the full automorphism group of the norm-trace curve 𝓒 : X(qr – 1)/(q–1) = Yqr–1 + Yqr–2 + … + Y is computed. Finally, these results are used to show that certain one-point AG codes have many automorphisms.

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