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Group (mathematics): Quiz

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Question 1: Such spontaneous symmetry breaking has found further application in elementary particle physics, where its occurrence is related to the appearance of ________.
Goldstone bosonPhotonTachyonFaddeev–Popov ghost

Question 2: Such symmetry groups, particularly the continuous ________, play an important role in many academic disciplines.
General linear groupGroup (mathematics)Lorentz groupLie group

Question 3: A standard example is the general linear group introduced above: it is an ________ of the space of all n-by-n matrices, because it is given by the inequality
Metric spaceTopological spaceTopologyOpen set

Question 4: Matrix groups consist of matrices together with ________.
Ring (mathematics)Vector spaceMatrix multiplicationField (mathematics)

Question 5: Groups for which the equation ab = ba always holds are called abelian (in honor of ________).
Carl Friedrich GaussNiels Henrik AbelChristopher HansteenAdrien-Marie Legendre

Question 6: In chemical fields, such as ________, space groups and point groups describe molecular symmetries and crystal symmetries.
Condensed matter physicsCrystallographyX-ray crystallographyAtom

Question 7: A broad class of ________ are linear representations, i.e.
Group (mathematics)Representation theoryGroup representationGroup theory

Question 8: Groups share a fundamental kinship with the notion of ________.
Group (mathematics)Symmetry (physics)Euclidean groupSymmetry

Question 9: [35] Further branches crucially applying groups include ________ and number theory.
TopologyAlgebraic geometryCalculusMathematics

Question 10: Expressed in words, adding a to b first, and then adding the result to c gives the same final result as adding a to the sum of b and c, a property known as ________.
AssociativityDistributivityCommutativityAlgebraic structure







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