Abstract
A finite group G is called smooth group if it has a maximal chain of subgroups in which any two intervals of the same length are isomorphic (as a lattice). A group G is called totally smooth group if all its maximal chains are smooth and is called generalized smooth if the chain [G/L] is totally smooth for every subgroup L of G of prime order. Let \(G_{p}\) be a Sylow p-subgroup of G. In this paper, we introduce the structure of a non-simple group G if \(|G_{p}|> p\) and all maximal subgroups of G whose order is divisible by the prime p are totally smooth groups (or generalized smooth groups) and hence we conclude an unexpected result which represents the main theorem of this paper.
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Communicated by Mikhail Belolipetsky.
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Abd-Ellatif, M.H. Finite groups with some generalized smooth maximal subgroups. São Paulo J. Math. Sci. (2024). https://doi.org/10.1007/s40863-024-00408-9
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DOI: https://doi.org/10.1007/s40863-024-00408-9