Covering Theorem for Alternating Groups

Sh. S. Al-Bundi

doi:10.30526/18.4.4406

October 20, 2005Ibn AL- Haitham Journal For Pure and Applied ScienceOpen Access

Covering Theorem for Alternating Groups

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Key Points

This research aims to explore the covering properties of alternating groups specifically focusing on contumacy classes of certain types.
Analyzed the contumacy class of type (2)(n-2) for n greater than 6 and even.
Applied theoretical frameworks to classify the cycles within the alternating groups.
Investigated the relationship between the classes C, C', and A.
Established that CCC covers A for the classes under study.
Identified a split in the contumacy class into two distinct classes C and C', refining the understanding of their structures.
Demonstrated significant implications for the covering phenomenon related to alternating groups.

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Implication

Brenner's work examines covering classes in alternating groups, revealing implications for group structure.

Abstract

For the alternating group An J. L. Brenner, through a series of papers showed that the class C of n- cycle or (n-1)- cycle, CCC covers A, for n = 4k - 1, 4k and 4k + 1, In this paper, the contumacy class of type (2)(n-2),n>6and n 1S even was studied. This class splits into two classes of A, c denoted by C and C, CCC= C'C'C was found.

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Sh. S. Al-Bundi (2005) studied this question.

synapsesocial.com/papers/698c1bef267fb587c655deb8 https://doi.org/10.30526/18.4.4406

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Covering Theorem for Alternating Groups

Key Points

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Implication

Abstract

Discussion

Cite This Study

Covering Theorem for Alternating Groups

Key Points

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Implication

Abstract

Discussion

Cite This Study

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