Onp-groups with odd order automorphism groups

1973 ◽  
Vol 24 (1) ◽  
pp. 465-471 ◽  
Author(s):  
Hermann Heineken ◽  
Hans Liebeck
Keyword(s):  
Automorphism Groups ◽  
Order Automorphism ◽  
Odd Order

scholarly journals Minimal odd order automorphism groups

2010 ◽  
Vol 13 (2) ◽  
Author(s):  
Peter Hegarty ◽  
Desmond MacHale
Keyword(s):  
Automorphism Groups ◽  
Order Automorphism ◽  
Odd Order

On Minimal Orders of Groups with Odd Order Automorphism Groups

2010 ◽  
Vol 39 (1) ◽  
pp. 199-208
Author(s):  
M. John Curran ◽  
Russell J. Higgs
Keyword(s):  
Automorphism Groups ◽  
Order Automorphism ◽  
Odd Order

scholarly journals Real order-automorphism groups

1981 ◽  
Vol 31 (3) ◽  
pp. 257-261 ◽  
Author(s):  
E. C. Weinberg
Keyword(s):  
Automorphism Groups ◽  
Real Numbers ◽  
Order Automorphism ◽  
Ordered Groups ◽  
Lattice Ordered Groups

AbstractBy using the concept of tame embeddings of chains, a characterization is given of the subobjects of the lattice-ordered groups of order-automorphisms of the chains of rational and real numbers.

On quasiprimitive edge-transitive graphs of odd order and twice prime valency

2020 ◽  
Vol 23 (6) ◽  
pp. 1017-1037
Author(s):  
Hong Ci Liao ◽  
Jing Jian Li ◽  
Zai Ping Lu
Keyword(s):  
Automorphism Group ◽  
Connected Graph ◽  
Automorphism Groups ◽  
Primitive Group ◽  
Odd Order ◽  
Vertex Set ◽  
Edge Transitive ◽  
Affine Type ◽  
Transitive Graphs

AbstractA graph is edge-transitive if its automorphism group acts transitively on the edge set. In this paper, we investigate the automorphism groups of edge-transitive graphs of odd order and twice prime valency. Let {\varGamma} be a connected graph of odd order and twice prime valency, and let G be a subgroup of the automorphism group of {\varGamma}. In the case where G acts transitively on the edge set and quasiprimitively on the vertex set of {\varGamma}, we prove that either G is almost simple, or G is a primitive group of affine type. If further G is an almost simple primitive group, then, with two exceptions, the socle of G acts transitively on the edge set of {\varGamma}.

scholarly journals Automorphisms and Enumeration of Switching Classes of Tournaments.

10.37236/1516 ◽  
2000 ◽  
Vol 7 (1) ◽  
Author(s):  
L. Babai ◽  
P. J. Cameron
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Probability Distributions ◽  
Explicit Construction ◽  
Linear Orders ◽  
Full Automorphism Group ◽  
Odd Order ◽  
Vertex Set ◽  
Countably Infinite ◽  
Switching Class

Two tournaments $T_1$ and $T_2$ on the same vertex set $X$ are said to be switching equivalent if $X$ has a subset $Y$ such that $T_2$ arises from $T_1$ by switching all arcs between $Y$ and its complement $X\setminus Y$. The main result of this paper is a characterisation of the abstract finite groups which are full automorphism groups of switching classes of tournaments: they are those whose Sylow 2-subgroups are cyclic or dihedral. Moreover, if $G$ is such a group, then there is a switching class $C$, with Aut$(C)\cong G$, such that every subgroup of $G$ of odd order is the full automorphism group of some tournament in $C$. Unlike previous results of this type, we do not give an explicit construction, but only an existence proof. The proof follows as a special case of a result on the full automorphism group of random $G$-invariant digraphs selected from a certain class of probability distributions. We also show that a permutation group $G$, acting on a set $X$, is contained in the automorphism group of some switching class of tournaments with vertex set $X$ if and only if the Sylow 2-subgroups of $G$ are cyclic or dihedral and act semiregularly on $X$. Applying this result to individual permutations leads to an enumeration of switching classes, of switching classes admitting odd permutations, and of tournaments in a switching class. We conclude by remarking that both the class of switching classes of finite tournaments, and the class of "local orders" (that is, tournaments switching-equivalent to linear orders), give rise to countably infinite structures with interesting automorphism groups (by a theorem of Fraïssé).

scholarly journals Large odd prime power order automorphism groups of algebraic curves in any characteristic

2020 ◽  
Vol 547 ◽  
pp. 312-344 ◽  
Author(s):  
Gábor Korchmáros ◽  
Maria Montanucci
Keyword(s):  
Prime Power ◽  
Algebraic Curves ◽  
Automorphism Groups ◽  
Prime Power Order ◽  
Order Automorphism

2-groups with an odd-order automorphism that is the identity on involutions

1969 ◽  
Vol 8 (6) ◽  
pp. 383-390 ◽  
Author(s):  
V. D. Mazurov
Keyword(s):  
Order Automorphism ◽  
Odd Order

ON FINITE p-GROUPS OF ODD ORDER WITH MANY SUBGROUPS 2-SUBNORMAL

1996 ◽  
Vol 24 (8) ◽  
pp. 2707-2719
Author(s):  
Gemma Parmeggiani ◽  
G. Zacher
Keyword(s):  
Odd Order
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