Size of free groups in varieties generated by finite groups
2019 ◽
Vol 29
(08)
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pp. 1419-1430
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The number of distinct [Formula: see text]-variable word maps on a finite group [Formula: see text] is the order of the rank [Formula: see text] free group in the variety generated by [Formula: see text]. For a group [Formula: see text], the number of word maps on just two variables can be quite large. We improve upon previous bounds for the number of word maps over a finite group [Formula: see text]. Moreover, we show that our bound is sharp for the number of 2-variable word maps over the affine group over fields of prime order and over the alternating group on five symbols.
2009 ◽
Vol 87
(3)
◽
pp. 329-357
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2012 ◽
Vol 49
(3)
◽
pp. 390-405
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1964 ◽
Vol 16
◽
pp. 435-442
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1999 ◽
Vol 60
(2)
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pp. 177-189
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1969 ◽
Vol 9
(3-4)
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pp. 467-477
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2017 ◽
Vol 16
(11)
◽
pp. 1750217
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2009 ◽
Vol 08
(02)
◽
pp. 229-242
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