Palindromic words in simple groups
2015 ◽
Vol 25
(03)
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pp. 439-444
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Keyword(s):
A palindrome is a word that reads the same left-to-right as right-to-left. We show that every simple group has a finite generating set X, such that every element of it can be written as a palindrome in the letters of X. Moreover, every simple group has palindromic width pw(G, X) = 1, where X only differs by at most one additional generator from any given generating set. On the contrary, we prove that all non-abelian finite simple groups G also have a generating set S with pw(G, S) > 1. As a by-product of our work we also obtain that every just-infinite group has finite palindromic width with respect to a finite generating set. This provides first examples of groups with finite palindromic width but infinite commutator width.
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2009 ◽
Vol 12
◽
pp. 82-119
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Keyword(s):
1995 ◽
Vol 51
(3)
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pp. 495-499
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Keyword(s):
2019 ◽
Vol 18
(04)
◽
pp. 1950070
Keyword(s):
2016 ◽
Vol 09
(03)
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pp. 1650054
2016 ◽
Vol 26
(4)
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pp. 628-640
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2007 ◽
Vol 17
(03)
◽
pp. 607-659
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1971 ◽
Vol 12
(4)
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pp. 385-392
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Keyword(s):
1998 ◽
Vol 58
(1)
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pp. 137-145
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