Question: What is a group labeled when the element 1 is primitive?
Answer: cyclic

Question: What group is isomorphic to cyclic groups?
Answer: Any cyclic group with n elements

Question: What example of cyclic group satisfies the express of zn = 1?
Answer: the group of n-th complex roots of unity

Question: What are groups consisting of symmetries of given arithmetic concepts?
Answer: Symmetry groups

Question: What term describes the introductory symmetry group of the square?
Answer: geometric nature

Question: What can regarded as the study of symmetry?
Answer: group theory

Question: What is the name of the rule that must be met for a group operation to occur?
Answer: group law

Question: The group pattern is connected to the structure of the target by what behavior?
Answer: group action

Question: What aids in predicting changes of physical traits?
Answer: group theory

Question: What stage of a physical transformation can group theory be used to make prediction?
Answer: phase transition

Question: What temperature causes the change of ferroelectric materials?
Answer: Curie temperature

Question: What term describes the vibrational lattice mode that turns to 0 frequency at the change?
Answer: soft phonon mode

Question: What are examples of finite symmetry groups used in coding theory?
Answer: Mathieu groups

Question: What is used for error correction of transferred data?
Answer: coding theory

Question: What describes functions having antiderivatives of a prescribed form?
Answer: differential Galois theory

Question: What concept investigates geometric elements that stay stable under group action?
Answer: invariant theory

Question: What groups combine matrices with matrix multiplication?
Answer: Matrix groups

Question: What includes all invertible n-by-n matrices with real entries?
Answer: The general linear group

Question: What term describes subgroups of the general linear group?
Answer: matrix groups

Question: What matrix group portrays all possible rotations in n dimensions?
Answer: the special orthogonal group SO(n)

Question: Rotation matrix groups are utilized in computer graphics with what concept?
Answer: Euler angles

Question: What degree does not include simple formulas for cubic and quatric equations?
Answer: degree 5 and higher

Question: What concept is associated with the solvability of polynomials?
Answer: Abstract properties of Galois groups

Question: What are used to express the solutions of polynomials?
Answer: radicals

Question: What does a finite group include?
Answer: a finite number of elements

Question: What is the number of elements in a group named?
Answer: the order of the group

Question: What type of class has a finite group that can be expressed as a subgroup of a symmetric group?
Answer: fundamental

Question: What can be described as the group of symmetries of an equilateral triangle?
Answer: S3

Question: What level of finality do mathematicians try to reach with math concepts? 
Answer: complete classification

Question: What area of classification leads to troublesome arithmetic?
Answer: finite groups

Question: What defines finite groups of order p, a prime number, as being necessarily cyclic (abelian) groups Zp?
Answer: Lagrange's theorem

Question: What can be used to classify small groups even though there is no classification of all finite groups?
Answer: Computer algebra systems

Question: What describes finite simple groups as the building pieces for all finite groups?
Answer: The Jordan–Hölder theorem

Question: What group operations must occur for group law and topology to integrate well?
Answer: continuous functions

Question: What is the most simple example of topological groups?
Answer: reals R under addition, (R ∖ {0}, ·),

Question: What variables do locally compact groups share that can be studied by harmonic analysis?
Answer: Haar measures

Question: What concepts are fundamental to number theory?
Answer: adele rings and adelic algebraic groups

Question: What group uses infinite field extensions with topology?
Answer: the absolute Galois group

Question: What is used to generalize the connection of fields and groups to infinite field extensions?
Answer: Krull topology

Question: What group is an advanced observation of infinite field extensions and groups that is adapted for the needs of algebraic geometry?
Answer: the étale fundamental group

Question: What concept is of basic importance in modern physics?
Answer: Lie groups

Question: What connects continuous symmetries to conserved quantities?
Answer: Noether's theorem

Question: What term describes the basic symmetries of the laws of mechanics?
Answer: Rotation

Question: What concept relates measurements of time and velocity of two observers in motion relative to each other?
Answer: Lorentz transformations

Question: What describe the complete symmetry group of Minkowski space including translations?
Answer: Poincaré group

Question: What product is created if the requirement that every element has an inverse is eliminated?
Answer: monoid

Question: What type of numbers under addition form a monoid?
Answer: natural numbers N (including 0)

Question: What method formally adds inverses to elements to any monoid?
Answer: the Grothendieck group

Question: What can be replaced to simplify abstract algebra concepts?
Answer: the binary operation

Question: Where is the Central African Republic located?
Answer: Central Africa

Question: What country borders CAR in the North?
Answer: Chad

Question: What Country borders CAR in the South?
Answer: the Republic of the Congo

Question: What Country borders CAR in the West?
Answer: Cameroon

Question: What is the population of CAR approximately?
Answer: 4.7 million

Question: Who established CAR's borders?
Answer: France

Question: What country ruled CAR as a colony?
Answer: France

Question: When did CAR become independent?
Answer: in 1960

Question: Who was the first democratically elected President?
Answer: Ange-Félix Patassé

Question: What religion is a minority in CAR?
Answer: Muslim minority

Question: How long ago did people start living in the area?
Answer: Approximately 10,000 years ago

Question: What agricultural job did people settling in the area perform?
Answer: farming

Question: What vegetation helped populations expand?
Answer: African oil palm

Question: What was an imported food that provided most of the carbohydrates?
Answer: Bananas

Question: What important protein helped with expansion of the inhabitants?
Answer: Fish

Question: When did the slave trade hit the CAR region?
Answer: 16th and 17th centuries

Question: What is one area where captive slaves were sent?
Answer: Europe

Question: Which people were major slave traders in the 19th century?
Answer: Bobangi people

Question: Who did the Bobangi sell slave to?
Answer: the Americas

Question: What river saw the establishment of a new Kingdom?
Answer: Ubangi River

Question: When was Equatorial Africa established?
Answer: 1920

Question: Where was Equatorial African ran from?
Answer: Brazzaville

Question: What plant was mandated to be grown by the French?
Answer: cotton

Question: What important infrastructure was built in the 1920s.
Answer: a network of roads

Question: What religion was spread through CAR?
Answer: Christianity

Question: During what war did French officers setup headquarters in CAR?
Answer: Second World War

Question: Who was elected in 1946 as the first representative?
Answer: Barthélémy Boganda

Question: How many votes did Boganda get?
Answer: 9,000 votes

Question: What was Bogandas platform that he ran for?
Answer: political stance against racism

Question: What caused Boganda to leave his elected post?
Answer: disheartened with the French political system

Question: What was the overwhelming amount of votes MESAN captured?
Answer: 347,000 out of the total 356,000 votes

Question: How many seats did MESAN win?
Answer: every legislative seat