We prove the existence of an additive semigroup of cardinality $2^\mathfrak c$ contained in the intersection of the classes of Hamel functions ($\rm HF$) and Sierpiński-Zygmund functions ($\rm SZ$). In addition, we show that under certain set-theoretic assumptions the lineability of the class of Sierpiński-Zygmund functions ($\rm SZ$) is equal to the lineability of the class of almost continuous Sierpiński-Zygmund functions ($\rm AC\cap\rm SZ$).
"Algebraic structures within subsets of Hamel and Sierpiński-Zygmund functions." Bull. Belg. Math. Soc. Simon Stevin 22 (3) 447 - 454, august 2015. https://doi.org/10.36045/bbms/1442364591