What question did this study set out to answer?

This research aims to explore the covering properties of alternating groups specifically focusing on contumacy classes of certain types.

February 11, 2026Open Access

Covering Theorem for Alternating Groups

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.

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.

Covering Theorem for Alternating Groups

Key Points

Abstract

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