On the structures of the Johnson cokernels of the basis-conjugating automorphism groups of free groups
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DOI: 10.1017/s0017089525100645
Abstract: In this article, we study the Johnson homomorphisms of basis-conjugating automorphism groups of free groups. We construct obstructions for the surjectivity of the Johnson homomorphisms. By using it, we determine their cokernels of degree up… read more here.
Keywords: groups free; basis conjugating; free groups; automorphism groups ... See more keywords
Freely indecomposable almost free groups with free abelianization
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DOI: 10.1515/jgth-2019-0102
Abstract: Abstract For certain uncountable cardinals κ, we produce a group of cardinality κ which is freely indecomposable, strongly κ-free, and whose abelianization is free abelian of rank κ. The construction takes place in Gödel’s constructible… read more here.
Keywords: abelianization; free groups; freely indecomposable; groups free ... See more keywords
On the Grossman representations of the automorphism groups of free groups
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DOI: 10.1515/jgth-2024-0161
Abstract: Abstract The goal of this paper is to show that, for any k ≥ 2 k\geq 2 , the subgroup of the automorphism group of a free group consisting of all automorphisms that act trivially… read more here.
Keywords: groups free; grossman representations; group; automorphism groups ... See more keywords