Probability and Bias in Generating Supersoluble Groups
2015 ◽
Vol 59
(4)
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pp. 899-909
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Keyword(s):
AbstractWe discuss some questions related to the generation of supersoluble groups. First we prove that the number of elements needed to generate a finite supersoluble groupGwith good probability can be quite a lot larger than the smallest cardinality d(G) of a generating set ofG. Indeed, ifGis the free prosupersoluble group of rankd⩾ 2 and dP(G) is the minimum integerksuch that the probability of generatingGwithkelements is positive, then dP(G) = 2d+ 1. In contrast to this, ifk–d(G) ⩾ 3, then the distribution of the first component in ak-tuple chosen uniformly in the set of all thek-tuples generatingGis not too far from the uniform distribution.
1983 ◽
Vol 35
(2)
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pp. 218-220
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Keyword(s):
1983 ◽
Vol 34
(2)
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pp. 265-268
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Keyword(s):
2019 ◽
pp. 131-160
Keyword(s):
2010 ◽
Vol 33
(5)
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pp. 900-907
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Keyword(s):