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We study monoids generated by Zariski-van Kampen generators in the 17fundamental groups of the complement of logarithmic free divisors in C^3 listedby Sekiguchi (Theorem 1). Five of them are Artin monoids and eight of them arefree abelian monoids. The remaining four monoids are not Gaussian and, hence,are neither Garside nor Artin (Theorem 2). However, we introduce, similarly toArtin monoids, fundamental elements and show their existence (Theorem 3). Oneof the four non-Gaussian monoids satisfies the cancellation condition (Theorem4).

Monoids in the fundamental groups of the complement of logarithmic free divisors in C^3