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A subgroup H of finite index in a group G (finite or infinite) always contains a normal subgroup N (of G), also of finite index. In fact, if H has index n, then the index of N will be some divisor of n! and a multiple of n; indeed, N can be taken to be the kernel of the natural homomorphism from G to the permutation group of the left (or right ...
Within each set of questions. users can take a random quiz or choose a specific topic on which to focus. Quizzes consist of multiple choice questions with four possible answers. After answering each question the user is given in-depth explanations of the answer and links to further reading.
Each question may contain from zero to three subsets of questions with marks ranging from 2 to 8 marks. The total weighting of the paper is 80 marks and constitutes 44% of the grade. Paper 2 (Duration: 2 hours 30 minutes): Questions are categorised into 3 sections: A, B and C. Section A contains 7 questions which must all be answered.
D.A. – D.B.A. – D.U.I. – D.W.I. – Damages – Damnation – Dangerous weapon – Data protection – Date rape – Daubert standard – Day in court – de bonis asportatis – de bonis non administratis – de facto – De facto corporation – de futuro – de integro – de jure – De jure corporation – de lege ferenda – de lege lata – de minimis – de novo – Deadlock ...
In addition, knowledge of the GCSE curriculum is assumed. [9] Paper 2: Mathematical Reasoning Paper 2 has 20 multiple-choice questions, with 75 minutes allowed to complete the paper. The second paper assesses a candidate’s ability to justify and interpret mathematical arguments and conjectures, and deal with elementary concepts from logic.
Computer model of the Banzhaf power index from the Wolfram Demonstrations Project. The Banzhaf power index, named after John Banzhaf (originally invented by Lionel Penrose in 1946 and sometimes called Penrose–Banzhaf index; also known as the Banzhaf–Coleman index after James Samuel Coleman), is a power index defined by the probability of changing an outcome of a vote where voting rights ...
A separate law of nature, the Lorentz force law, describes how the electric and magnetic fields act on charged particles and currents. By convention, a version of this law in the original equations by Maxwell is no longer included. The vector calculus formalism below, the work of Oliver Heaviside, [6] [7] has become standard.
Zipf's law (/ z ɪ f /; German pronunciation:) is an empirical law stating that when a list of measured values is sorted in decreasing order, the value of the n-th entry is often approximately inversely proportional to n. The best known instance of Zipf's law applies to the frequency table of words in a text or corpus of natural language: