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If a group has nilpotency class at most n, then it is sometimes called a nil-n group. It follows immediately from any of the above forms of the definition of nilpotency, that the trivial group is the unique group of nilpotency class 0, and groups of nilpotency class 1 are exactly the non-trivial abelian groups. [2] [3]
A non-trivial effort is required for the reader to traverse the text, as the reader must constantly select which link to follow, but a link, when clicked, will always lead to the same node. A chat bot such as ELIZA is a cybertext because when the reader types in a sentence, the text-machine actually performs calculations on the fly that ...
"A science fiction story is a story built around human beings, with a human problem, and a human solution, which would not have happened at all without its scientific content." [13] Basil Davenport. 1955. "Science fiction is fiction based upon some imagined development of science, or upon the extrapolation of a tendency in society." [14] Edmund ...
Science fiction genre – while science fiction is a genre of fiction, a science fiction genre is a subgenre within science fiction. Science fiction may be divided along any number of overlapping axes. Gary K. Wolfe's Critical Terms for Science Fiction and Fantasy identifies over 30 subdivisions of science fiction, not including science fantasy ...
Science fiction (sometimes shortened to sci-fi or abbreviated SF) is a genre of speculative fiction which typically deals with imaginative and futuristic concepts such as advanced science and technology, space exploration, time travel, parallel universes, and extraterrestrial life.
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Indeed, for p-groups, the rank of the group P is the dimension of the vector space P/Φ(P), where Φ(P) is the Frattini subgroup. The rank of a group is also often defined in such a way as to ensure subgroups have rank less than or equal to the whole group, which is automatically the case for dimensions of vector spaces, but not for groups such ...
Once these are known, the ones with non-trivial center are easy to list as follows. Any simple Lie group with trivial center has a universal cover whose center is the fundamental group of the simple Lie group. The corresponding simple Lie groups with non-trivial center can be obtained as quotients of this universal cover by a subgroup of the ...