On the nX-Complementary Generation of the Projective Symplectic Group PSp(4,5)

Document Type : Original Article

Authors

Ayoub Basheer Mohammed Basheer ¹

Mahlare Gerald Sehoana ²

¹ School of Mathematical and Computer Sciences‎, ‎University of Limpopo (Turfloop)‎, ‎P Bag X1106‎, ‎Sovenga 0727‎, ‎South Africa

² Mathematics Program‎, ‎Faculty of Education and Arts‎, ‎Sohar University‎, ‎P‎. ‎O‎. ‎Box 311‎, ‎Sohar‎, ‎Oman

10.22067/kjm.2026.565467.3758

Abstract

This paper classifies all the non-trivial conjugacy classes of the finite simple symplectic group PSp(4, 5) whether they are complementary generators or not. A group G is said to be nX-complementary generated if given an arbitrary non-identity element x in G, then there exists an element y in nX such that G = ⟨x, y⟩. The group PSp(4, 5) is nX-complementary generated for n = 5, 12, 13, 15, 20, 30, with nX not in the set {5A, 5B, 5C, 5D}. The proof combines the structure constant method from the character table, detailed analysis of the group’s maximal subgroups, and applications of Scott’s Theorem and other generation criteria. Computational support from GAP is used extensively to calculate structure constants and verify generation.

Keywords

Conjugacy classes

complementary generation

structure constants

Symplectic group

Subjects

• 20 Group theory and generalizations

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