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In mathematics, specifically group theory, given a prime number p, a p-group is a group in which the order of every element is a power of p.That is, for each element g of a p-group G, there exists a nonnegative integer n such that the product of p n copies of g, and not fewer, is equal to the identity element.
Cauchy's theorem is generalized by Sylow's first theorem, which implies that if p n is the maximal power of p dividing the order of G, then G has a subgroup of order p n (and using the fact that a p-group is solvable, one can show that G has subgroups of order p r for any r less than or equal to n).
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I do not / I don't I’ve: I have isn’t: is not it’d: it would it’ll: it shall / it will it’s: it has / it is Idunno (informal) I do not know kinda (informal) kind of lemme: let me let’s: let us loven’t (informal) love not (colloquial) ma’am (formal) madam mayn’t: may not may’ve: may have methinks (informal) I think mightn’t ...
Isotherms of an ideal gas for different temperatures. The curved lines are rectangular hyperbolae of the form y = a/x. They represent the relationship between pressure (on the vertical axis) and volume (on the horizontal axis) for an ideal gas at different temperatures: lines that are farther away from the origin (that is, lines that are nearer to the top right-hand corner of the diagram ...
Their negations, shall not and will not, also have contracted forms: shan't and won't (although shan't is rarely used in North America, and is becoming rarer elsewhere too). See English auxiliaries and contractions. The pronunciation of will is / w ɪ l /, and that of won't is / w oʊ n t /.
where H is the enthalpy, T the absolute temperature and G the Gibbs free energy of the system, all at constant pressure p. The equation states that the change in the G/T ratio at constant pressure as a result of an infinitesimally small change in temperature is a factor H/T 2. Similar equations include [6]
In other words, any problem in EXPTIME is solvable by a deterministic Turing machine in O(2 p(n)) time, where p(n) is a polynomial function of n. A decision problem is EXPTIME-complete if it is in EXPTIME, and every problem in EXPTIME has a polynomial-time many-one reduction to it. A number of problems are known to be EXPTIME-complete.