http://www.tac.mta.ca/tac/reprints/articles/7/tr7abs.html

I think it is interesting that Philip was able by using groupoids to get this generalisation, which seems not to have been reached by the methods traditionally used in group theory to prove Grusko’s theorem.

Again, the statement of van Kampen’s theorem in this blog refers only to the version for the fundamental group, and not to the many base point version. I was kind of irritated in the 1960s that the standard version of this theorem could not even compute the fundamental group of the circle, a basic example, and saw this as an anomaly to be repaired somehow. This starting point eventually opened up for me large areas of research!

]]>Here is Higgins’ Theorem.

Let be groups with free decompositions , (), and let be a group morphism such that

for all .

Let be a subgroup of such that . Then

has a decomposition such that for all .

Higgins’ book is a free download.

See also

Braun, G. A proof of Higgins’s conjecture. Bull. Austral. Math. Soc 70~(2) (2004) 207–212.

]]>Higgins, P.J._Notes on categories and groupoids_ , _Mathematical Studies_ , Volume 32. Van Nostrand Reinhold Co London (1971).; Reprints in _Theory and Applications of Categories_, No. 7 (2005) pp 1-195,

following his 1966 paper in J. Algebra. 4 (1966) 365–372.

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