Finite groups whose subgroup graph contains a vertex of large degree

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2025年4月4日

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Marius Tărnăuceanu

摘要

Burness and Scott (J Aust Math Soc 87:329-357, 2009) classified finite groups G such that the number of prime order subgroups of G is greater than $|G|/2-1$ $| G | / 2 - 1$ . In this note, we study finite groups G whose subgroup graph contains a vertex of degree greater than $|G|/2-1$ $| G | / 2 - 1$ . The classification given for finite solvable groups extends the work of Burness and Scott.