Odd Order Group Actions and Witt Classification of Innerproducts

1977 ◽  
Author(s):  
John P. Alexander ◽  
Pierre E. Conner ◽  
Gary C. Hamrick
Keyword(s):  
Group Actions ◽  
Order Group ◽  
Odd Order

Inequivalent, bordant group actions on a surface

1986 ◽  
Vol 99 (2) ◽  
pp. 233-238 ◽  
Author(s):  
Charles Livingston
Keyword(s):  
Fixed Point ◽  
Finite Groups ◽  
Group Actions ◽  
Free Actions ◽  
Orientable Surfaces

An action of a group, G, on a surface, F, consists of a homomorphismø: G → Homeo (F).We will restrict our discussion to finite groups acting on closed, connected, orientable surfaces, with ø(g) orientation-preserving for all g ε G. In addition we will consider only effective (ø is injective) free actions. Free means that ø(g) is fixed-point-free for all g ε G, g ≠ 1. This paper addresses the classification of such actions.

scholarly journals PARAMETERS OF INTEGRAL CIRCULANT GRAPHS AND PERIODIC QUANTUM DYNAMICS

2007 ◽  
Vol 05 (03) ◽  
pp. 417-430 ◽  
Author(s):  
NITIN SAXENA ◽  
SIMONE SEVERINI ◽  
IGOR E. SHPARLINSKI
Keyword(s):  
Quantum Dynamics ◽  
Perfect State ◽  
Circulant Graph ◽  
Circulant Graphs ◽  
Odd Order ◽  
State Transfer ◽  
Network Topologies ◽  
Perfect State Transfer ◽  
Exact Bounds

The intention of the paper is to move a step towards a classification of network topologies that exhibit periodic quantum dynamics. We show that the evolution of a quantum system whose hamiltonian is identical to the adjacency matrix of a circulant graph is periodic if and only if all eigenvalues of the graph are integers (that is, the graph is integral). Motivated by this observation, we focus on relevant properties of integral circulant graphs. Specifically, we bound the number of vertices of integral circulant graphs in terms of their degree, characterize bipartiteness and give exact bounds for their diameter. Additionally, we prove that circulant graphs with odd order do not allow perfect state transfer.

scholarly journals On the Modular Version of Ito’s Theorem on Character Degrees for Groups of Odd Order

1987 ◽  
Vol 105 ◽  
pp. 109-119 ◽  
Author(s):  
Olaf Manz
Keyword(s):  
Finite Group ◽  
Representation Theory ◽  
Prime Number ◽  
Character Degrees ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Classical Representation ◽  
Odd Order ◽  
Complex Characters

One of the most useful theorems in classical representation theory is a result due to N. Ito, which can be stated using the classification of the finite simple groups in the following way.THEOREM (N. Ito, G. Michler). Let Irr (G) be the set of all irreducible complex characters of the finite group G and q be a prime number. Then if and only if G has a normal, abelian Sylow-q-subgroup.

scholarly journals Prevalência de ações táticas ofensivas de grupo no Campeonato Brasileiro de Futebol Série A (2018 e 2019)

2021 ◽  
Vol 19 (2) ◽  
pp. 1-5
Author(s):  
Allan Gabriel Silva Nascimento ◽  
João Marcelo Niquini Caríssimo ◽  
César Milagres Silva ◽  
Siomara Aparecida Silva
Keyword(s):  
Group Actions ◽  
Correlation Test

INTRODUÇÃO: O futebol é um dos esportes mais populares, sendo a tática um dos quesitos fundamentais para o sucesso. OBJETIVO: Identificar a associação entre os quantitativos das ações táticas ofensivas de grupo e os parâmetros de resultados das equipes mais bem colocadas no Campeonato Brasileiro Série A, temporadas 2018 e 2019.  MÉTODOS: Analisaram-se as seis equipes primeiras colocadas do Campeonato Brasileiro de Futebol Série A 2018 e 2019. O instrumento utilizado foi o Footstats. Foi realizada a análise descritiva das ações táticas ofensivas de grupo e a correlação de Spearman rho entre as variáveis das ações táticas com gols pró e pontos por meio do SPSS™ v. 23. RESULTADOS: A ação tática ofensiva de grupo “virada de bola” obteve associações significativas com “pontos” (r=0,829; p=0,042) e “gols pró” (r=0,943; p=0,005) no campeonato de 2018. No campeonato de 2019, as ações táticas ofensivas de grupo “assistências” e “cruzamentos” evidenciaram associação significativa com “pontos” (r=0,812; p=0,050 e r=0,928; p=0,008, respectivamente), “gols pró” com “virada de bola” (r=0,943; p=0,005) e “pontos” (r=0,812; p=0,050). CONCLUSÃO: As ações táticas ofensivas de grupo associaram-se com gols pró e pontos na classificação final das primeiras equipes em ambos os anos. Destaca-se a “virada de bola” no campeonato de 2018, além de “assistências” e “cruzamento” na edição de 2019, como ações que podem ser relevantes para a conquista dos pontos e por consequência melhores resultados dentro de tais competições.ABSTRACT. Prevalence of offensive tactical group actions in the Brazilian Football Championship A Series (2018-2019)BACKGROUND: Soccer is one of the most popular sports worldwide, with tactics being one of the fundamental requirements for teams to succeed in this sport. OBJECTIVE: o identify the association between the quantitative of the group’s offensive tactical actions and the parameters of result of the top six teams of the A-Series Brazilian Football Championship, seasons 2018 and 2019. METHODS: The top six teams of the two seasons were analyzed. The instrument employed was the software Footstats. Descriptive and correlation analyzes were carried out, together with Spearman rho correlation test between the variables of the group’s offensive tactical actions and the parameters of goals pro and points. RESULTS: The offensive tactical action “switch sides” obtained significant associations with “points” (r=0.829; p=0.042) and “goals for” (r=0.943; p=0.005) in the 2018 season. In 2019, the offensive tactical actions “assistances” and “crosses” evidenced significant associations with “points” (r=0.812; p=0.050 and r=0.928; p=0.008, respectively), as well as “goals for” with “switch sides” (R=0.943; p=0.005) and “points” (r=0.812; p=0.050). CONCLUSION: The number of groups offensive tactical actions were associated with the number of goals pro and points in the final classification of the top teams of both seasons. The actions “switch sides” in season 2018, besides “assistances” and “crosses” in season 2019 appeared as relevant for the achievements of points and, consequently, better results in such competitions.

scholarly journals Antiautomorphisms and Biantiautomorphisms of Some Finite Abelian Groups

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 294
Author(s):  
Daniel López-Aguayo ◽  
Servando López Aguayo
Keyword(s):  
Lower Bound ◽  
Abelian Groups ◽  
Additive Group ◽  
Exact Formula ◽  
Finite Abelian Groups ◽  
Cyclic Groups ◽  
Partial Classification ◽  
Open Questions ◽  
Odd Order

We extend the concepts of antimorphism and antiautomorphism of the additive group of integers modulo n, given by Gaitanas Konstantinos, to abelian groups. We give a lower bound for the number of antiautomorphisms of cyclic groups of odd order and give an exact formula for the number of linear antiautomorphisms of cyclic groups of odd order. Finally, we give a partial classification of the finite abelian groups which admit antiautomorphisms and state some open questions.

scholarly journals A complete classification of dynamical symmetries in classical mechanics

1985 ◽  
Vol 32 (2) ◽  
pp. 299-308 ◽  
Author(s):  
Geoff Prince
Keyword(s):  
Differential Equation ◽  
Variational Formulation ◽  
Order Differential Equation ◽  
Classical Mechanics ◽  
Group Actions ◽  
Complete Classification ◽  
Invariance Group ◽  
Dynamical Symmetries ◽  
Second Order Differential Equation

This paper deals with the interaction between the invariance group of a second order differential equation and its variational formulation. In particular I construct equivalent Lagrangians from all such group actions, thereby successfully completing an earlier attempt of mine which dealt with some traditionally important classes of actions.

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