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For example, the torsion subgroup tG is always a pure subgroup of G (this is a routine check) but it is not necessarily a direct summand of G. Suppose that G is an abelian group..
Reflective obstructions, that is branch divisors, are a special problem related to the orthogonal group. They do not appear in the case of moduli spaces of polarised abelian
In the case where N is a cyclic group, we will try to exploit the fact that we know Amitsur’s conjecture to be true for N crossed products to prove the conjecture for G
2.1.2], where K/k is a Galois extension of number fields of group G, and also coincides in the abelian case with the function field case of [8, Conj.. We recall that the vanishing of
By definition, a symmetric categor- ical group is a categorification of an abelian group, and in this sense the 2-category of symmetric categorical groups SCG can be regarded as
Using the Van Kampen type theorem for the fundamen- tal crossed module, applications are given to the 2-types of mapping cones of classifying spaces of groups.. Calculations of
A coefficient short exact sequence of crossed G-R-bimodules gives rise to a nine-term exact co- homology sequence and we recover the exact cohomology sequence obtained in [1] when
We introduce the notion of (pre)crossed module in a semiabelian category, and establish equivalences between internal reflexive graphs and precrossed modules, and between
