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Subgroups which admit extensions of homomorphisms
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Published/Copyright:
September 12, 2013
Abstract
We classify by numerical invariants the finite subgroups H of a primary abelian group G for which every homomorphism or monomorphism of H into G, or every endomorphism of H, extends to an endomorphism of G. We apply these results to show that for finitely generated subgroups of general abelian groups, the extendibility of monomorphisms implies the extendibility of all homomorphisms.
Funding source: CNCS-UEFISCDI
Award Identifier / Grant number: PN-II-RU-TE-2011-3-0065
Received: 2013-5-30
Published Online: 2013-9-12
Published in Print: 2015-9-1
© 2015 by De Gruyter
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- On Wolff's L5/2-Kakeya maximal inequality in ℝ3
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Articles in the same Issue
- Frontmatter
- Subgroups which admit extensions of homomorphisms
- On the Dedekind completion of function rings
- Semiperfect and coreflexive coalgebras
- Approximations to the Karcher mean on Hadamard spaces via geometric power means
- Separable convolution-elliptic operators with parameters
- Charged spaces
- Autotopies and quasigroup identities: New aspects of non-associative division algebras
- Dualizing complexes and homomorphisms vanishing in Koszul homology
- Comparison tests for the asymptotic behaviour of higher-order dynamic equations of neutral type
- Hardy spaces associated with a pair of commuting operators
- Weighted multilinear Hardy operators and commutators
- A characterisation of almost simple groups with socle 2E6(2) or M(22)
- The Σ1-invariant for Artin groups of circuit rank 1
- The average signature of graph links
- Peetre's theorem in the locally convex setting
- Small covers, infra-solvmanifolds and curvature
- Farrell–Jones spheres and inertia groups of complex projective spaces
- Character sums over unions of intervals
- Cones of certain isolated left orderings and chain domains
- On Wolff's L5/2-Kakeya maximal inequality in ℝ3
- Fractional type Marcinkiewicz integral operators on function spaces
- Lévy–Khintchine type representation of Dirichlet generators and semi-Dirichlet forms
- Homogeneous (α,β)-metrics of Douglas type
