- In mathematics, a
Hopfian group is a
group G for
which every epimorphism G → G is an isomorphism. Equivalently, a
group is
Hopfian if and only if it is...
- In the
branch of
mathematics called category theory, a
hopfian object is an
object A such that any
epimorphism of A onto A is
necessarily an automorphism...
-
group theory, a co-
Hopfian group is a
group that is not
isomorphic to any of its
proper subgroups. The
notion is dual to that of a
Hopfian group,
named after...
-
examples of non-
Hopfian groups. The
groups contain residually finite groups,
Hopfian groups that are not
residually finite, and non-
Hopfian groups. Define...
- in the
field of pure mathematics. Co-
Hopfian group Cohomotopy group EHP
spectral sequence Hopfian group Hopfian object Quantum group Alexandroff P., Hopf...
-
generated residually finite groups are
Hopfian groups. For
example the Baumslag–Solitar
group B(2,3) is not
Hopfian, and
therefore not
residually finite...
-
automorphism of M. This says
simply that M is a
Hopfian module. Similarly, an
Artinian module M is co
Hopfian: any
injective endomorphism f is also a surjective...
-
contradicting the degree-1 ****umption. This
implies that the
conjecture holds for
Hopfian groups, as for them one then gets that f ∗ {\displaystyle f_{*}} is an...
- the
property of
being Hopfian is
undecidable for
finitely presentable groups,
while neither being Hopfian nor
being non-
Hopfian are Markov. Higman's embedding...
-
Gilbert Baumslag and
Donald Solitar, Some two-generator one-relator non-
Hopfian groups,
Bulletin of the
American Mathematical Society 68 (1962), 199–201...
