Symmetry groups are groups consisting of symmetries of given mathematical objects—be they of geometric nature, such as the introductory symmetry group of the square, or of algebraic nature, such as polynomial equations and their solutions. Conceptually, group theory can be thought of as the study of symmetry.t[›] Symmetries in mathematics greatly simplify the study of geometrical or analytical objects. A group is said to act on another mathematical object X if every group element performs some operation on X compatibly to the group law. In the rightmost example below, an element of order 7 of the (2,3,7) triangle group acts on the tiling by permuting the highlighted warped triangles (and the other ones, too). By a group action, the group pattern is connected to the structure of the object being acted on.
What can regarded as the study of symmetry?
group theory

On 6 April 1941, German forces, with Hungarian and Italian assistance, launched an invasion of Yugoslavia. On 10 April 1941, Slavko Kvaternik proclaimed the Independent State of Croatia, and Tito responded by forming a Military Committee within the Central Committee of the Yugoslav Communist Party. Attacked from all sides, the armed forces of the Kingdom of Yugoslavia quickly crumbled. On 17 April 1941, after King Peter II and other members of the government fled the country, the remaining representatives of the government and military met with the German officials in Belgrade. They quickly agreed to end military resistance. On 1 May 1941, Tito issued a pamphlet calling on the people to unite in a battle against the occupation. On 27 June 1941, the Central Committee of the Communist Party of Yugoslavia appointed Tito Commander in Chief of all project national liberation military forces. On 1 July 1941, the Comintern sent precise instructions calling for immediate action.
What did Tito use to get the people to unit in a battle against the occupation in 1941?
pamphlet

Hidalgo was turned over to the Bishop of Durango, Francisco Gabriel de Olivares, for an official defrocking and excommunication on July 27, 1811. He was then found guilty of treason by a military court and executed by firing squad on July 30 at 7 in the morning. Before his execution, he thanked his jailers, Private Soldiers Ortega and Melchor, in letters for their humane treatment. At his execution, Hidalgo placed his right hand over his heart to show the riflemen where they should aim. He also refused the use of a blindfold. His body, along with the bodies of Allende, Aldama and José Mariano Jiménez were decapitated, and the heads were put on display on the four corners of the Alhóndiga de Granaditas in Guanajuato. The heads remained there for ten years until the end of the Mexican War of Independence to serve as a warning to other insurgents. Hidalgo's headless body was first displayed outside the prison but then buried in the Church of St Francis in Chihuahua. Those remains would later be transferred in 1824 to Mexico City.
In which year was Hidalgo turned over?
1811