Central elements in core-free groups
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In this paper, the authors established sufficient conditions for a finite group to have a nontrivial center or a normal subgroup of odd order in order to be core-free in finite groups.About:
This article is published in Journal of Algebra.The article was published on 1966-11-01 and is currently open access. It has received 442 citations till now. The article focuses on the topics: Normal subgroup & Centralizer and normalizer.read more
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Fusion Systems in Algebra and Topology
TL;DR: A fusion system over a p-group is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups as mentioned in this paper.
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2-Fusion in Finite Groups
TL;DR: In this paper, the composition factors of AG, the normal closure of A in G, when G is an S(A)-group were determined for the case where G is finite, T is a Sylow 2-subgroup of G, and A is Abelian.
References
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The theory of groups
TL;DR: The theory of normal subgroups and homomorphisms was introduced in this article, along with the theory of $p$-groups regular $p-groups and their relation to abelian groups.
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Representation Theory of Finite Groups and Associative Algebras
Charles W. Curtis,Irving Reiner +1 more
TL;DR: In this paper, the authors present a group theory representation and modular representation for algebraic number theory, including Semi-Semi-Simple Rings and Group Algebras, including Frobenius Algebraic numbers.
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Some applications of the theory of blocks of characters of finite groups. II
TL;DR: In this article, it was shown that a 2-Sylow group of a Zgroup P can be shown to have a center of order 2 in the form of an element v of P and two involutions (i.e., elements of order 1) y1, yz of P. In Section 1'11, a simplified proof is given.