Nilpotent 1‐factorizations of the complete graph | Zendy

Rinaldi Gloria | Zendy

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Nilpotent 1‐factorizations of the complete graph

Author(s) -

Rinaldi Gloria

Publication year - 2005

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.20069

Subject(s) - mathematics , sylow theorems , combinatorics , abelian group , p group , automorphism , factorization , vertex (graph theory) , discrete mathematics , nilpotent , graph , group (periodic table) , finite group , chemistry , organic chemistry , algorithm

For which groups G of even order 2 n does a 1‐factorization of the complete graph K 2n exist with the property of admitting G as a sharply vertex‐transitive automorphism group? The complete answer is still unknown. Using the definition of a starter in G introduced in 4, we give a positive answer for new classes of groups; for example, the nilpotent groups with either an abelian Sylow 2‐subgroup or a non‐abelian Sylow 2‐subgroup which possesses a cyclic subgroup of index 2. Further considerations are given in case the automorphism group G fixes a 1‐factor. © 2005 Wiley Periodicals, Inc. J Combin Designs

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