Question: The concept of a group arose from the study of polynomial equations, starting with Evariste Galois in the 1830s. After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Modern group theoryan active mathematical disciplinestudies groups in their own right.a["] To explore groups, mathematicians have devised various notions to break groups into smaller, better-understandable pieces, such as subgroups, quotient groups and simple groups. In addition to their abstract properties, group theorists also study the different ways in which a group can be expressed concretely (its group representations), both from a theoretical and a computational point of view. A theory has been developed for finite groups, which culminated with the classification of finite simple groups announced in 1983.aa["] Since the mid-1980s, geometric group theory, which studies finitely generated groups as geometric objects, has become a particularly active area in group theory.
Is there an answer to this question: What year did mathematicians begin studying groups in their own right?

Answer: unanswerable

Question: The Football Association Premier League Ltd (FAPL) is operated as a corporation and is owned by the 20 member clubs. Each club is a shareholder, with one vote each on issues such as rule changes and contracts. The clubs elect a chairman, chief executive, and board of directors to oversee the daily operations of the league. The current chairman is Sir Dave Richards, who was appointed in April 1999, and the chief executive is Richard Scudamore, appointed in November 1999. The former chairman and chief executive, John Quinton and Peter Leaver, were forced to resign in March 1999 after awarding consultancy contracts to former Sky executives Sam Chisholm and David Chance. The Football Association is not directly involved in the day-to-day operations of the Premier League, but has veto power as a special shareholder during the election of the chairman and chief executive and when new rules are adopted by the league.
Is there an answer to this question: Who is owned by over 20 member clubs?

Answer: unanswerable

Question: John's lack of religious conviction has been noted by contemporary chroniclers and later historians, with some suspecting that John was at best impious, or even atheistic, a very serious issue at the time. Contemporary chroniclers catalogued his various anti-religious habits at length, including his failure to take communion, his blasphemous remarks, and his witty but scandalous jokes about church doctrine, including jokes about the implausibility of the Resurrection. They commented on the paucity of John's charitable donations to the church. Historian Frank McLynn argues that John's early years at Fontevrault, combined with his relatively advanced education, may have turned him against the church. Other historians have been more cautious in interpreting this material, noting that chroniclers also reported John's personal interest in the life of St Wulfstan of Worcester and his friendships with several senior clerics, most especially with Hugh of Lincoln, who was later declared a saint. Financial records show a normal royal household engaged in the usual feasts and pious observances albeit with many records showing John's offerings to the poor to atone for routinely breaking church rules and guidance. The historian Lewis Warren has argued that the chronicler accounts were subject to considerable bias and the King was "at least conventionally devout," citing his pilgrimages and interest in religious scripture and commentaries.
Is there an answer to this question: Many records showed what?

Answer: John's offerings to the poor

Question: According to the American National Standards Institute, pitch is the auditory attribute of sound according to which sounds can be ordered on a scale from low to high. Since pitch is such a close proxy for frequency, it is almost entirely determined by how quickly the sound wave is making the air vibrate and has almost nothing to do with the intensity, or amplitude, of the wave. That is, "high" pitch means very rapid oscillation, and "low" pitch corresponds to slower oscillation. Despite that, the idiom relating vertical height to sound pitch is shared by most languages. At least in English, it is just one of many deep conceptual metaphors that involve up/down. The exact etymological history of the musical sense of high and low pitch is still unclear. There is evidence that humans do actually perceive that the source of a sound is slightly higher or lower in vertical space when the sound frequency is increased or decreased.
Is there an answer to this question: High pitch is what type of oscillation?

Answer:
rapid