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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 ...
To list terms and definitions, start a new line with a semicolon (;) followed by the term. Then, type a colon (:) followed by a definition. The format can also be used for other purposes, such as make and models of vehicles, etc. Description lists (formerly definition lists, and a.k.a. association lists) consist of group names corresponding to ...
The second method is used when the number of elements in each row is the same and known at the time the program is written. The programmer declares the array to have, say, three columns by writing e.g. elementtype tablename[][3];. One then refers to a particular element of the array by writing tablename[first index][second index]. The compiler ...
In group theory, a word is any written product of group elements and their inverses. For example, if x, y and z are elements of a group G, then xy, z −1 xzz and y −1 zxx −1 yz −1 are words in the set {x, y, z}. Two different words may evaluate to the same value in G, [1] or even in every group. [2]
The identity of a subgroup is the identity of the group: if G is a group with identity e G, and H is a subgroup of G with identity e H, then e H = e G. The inverse of an element in a subgroup is the inverse of the element in the group: if H is a subgroup of a group G, and a and b are elements of H such that ab = ba = e H, then ab = ba = e G.
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An access key allows a computer user to immediately jump to a specific part of a web page via the keyboard. On Wikipedia, access keys allow you to do a lot more—protect a page, show page history, publish your changes, show preview text, and so on.
Shortcut Action; Mark as Read K: Mark as Unread Shift + K: Star L: Unstar Shift + L: Delete Del or Backspace: Archive E: Restore to inbox Shift + E: Open Move menu D: Go to the previous message Left arrow: Go to the next message Right arrow: Reply R: Reply all A: Forward F: Print P: Open attachmet preview Shift + P