Degrees of compression and inertia for free-abelian times free groups
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DOI: 10.1016/j.jalgebra.2020.09.040
Abstract: We introduce the concepts of degree of inertia, $\text{di}_G(H)$, and degree of compression, $\text{dc}_G(H)$, of a finitely generated subgroup $H$ of a given group $G$. For the case of direct products of free-abelian and free… read more here.
Keywords: inertia; free abelian; degree inertia; free groups ... See more keywords
Generating the inverse limit of free groups
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DOI: 10.1016/j.jalgebra.2021.02.017
Abstract: Abstract We study the relation between two uncountable groups with remarkable properties (cf. [15] ): the topological free product of infinite cyclic groups G , and the inverse limit of finitely generated free groups F… read more here.
Keywords: free groups; limit free; generating inverse; inverse limit ... See more keywords
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