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Principal blocks and p -radical groups

Xiaohan Hu, Jiwen Zeng (2016)

Czechoslovak Mathematical Journal

Let G be a finite group and k a field of characteristic p > 0 . In this paper, we obtain several equivalent conditions to determine whether the principal block B 0 of a finite p -solvable group G is p -radical, which means that B 0 has the property that e 0 ( k P ) G is semisimple as a k G -module, where P is a Sylow p -subgroup of G , k P is the trivial k P -module, ( k P ) G is the induced module, and e 0 is the block idempotent of B 0 . We also give the complete classification of a finite p -solvable group G which has not more than three...

Principal bundles, groupoids, and connections

Anders Kock (2007)

Banach Center Publications

We clarify in which precise sense the theory of principal bundles and the theory of groupoids are equivalent; and how this equivalence of theories, in the differentiable case, reflects itself in the theory of connections. The method used is that of synthetic differential geometry.

Principal congruence link complements

Mark D. Baker, Alan W. Reid (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

In this paper we study principal congruence link complements in S 3 . It is known that there are only finitely many such link complements, and we make a start on enumerating them using a combination of theoretical methods and computer calculations with MAGMA.

Principal ideals of finitely generated commutative monoids

José Carlos Rosales, Juan Ignacio García-García (2002)

Czechoslovak Mathematical Journal

We study the semigroups isomorphic to principal ideals of finitely generated commutative monoids. We define the concept of finite presentation for this kind of semigroups. Furthermore, we show how to obtain information on these semigroups from their presentations.

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