Abstract
Let G be a finite group and X be a conjugacy class of G. The rank of X in G, denoted by rank(G : X), is defined to be the minimal number of elements of X generating G. In this paper we establish some general results on the ranks of certain conjugacy classes of elements for simple alternating group \(A_{n}\). We apply these general results together with the structure constants method to determine the ranks of all the non-trivial classes of \(A_{8}\) and \(A_{9}\).
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Acknowledgements
The first author would like to thank his supervisor (second author) for his assistance and guidance. He also would like to thank the North-West University and the National Research Foundation (NRF) of South Africa for the financial support received.
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Kar Ping Shum.
Ayoub B. M. Basheer is currently a postdoctoral fellow at the North-West University, Mafikeng Campus. Jamshid Moori: Support of National Research Foundation (NRF) of South Africa and the North-West University (Mafikeng) is acknowledged.
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Basheer, A.B.M., Moori, J. On the Ranks of the Alternating Group \(A_{n}\). Bull. Malays. Math. Sci. Soc. 42, 1957–1973 (2019). https://doi.org/10.1007/s40840-017-0586-5
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DOI: https://doi.org/10.1007/s40840-017-0586-5