We prove that Cayley graphs of SL2 (Fp ) are expanders with respect to the projection of any ﬁxed elements in SL(2, Z) generating a non-elementary subgroup, and with respect to generators chosen at random in SL2 (Fp ). 1. Introduction Expanders are highly-connected sparse graphs widely used in computer science, in areas ranging from parallel computation to complexity theory and cryptography; recently they also have found some remarkable applications in pure mathematics; see ,, , ,  and references therein. ...
The atomic theory of matter asserts that material bodies are made up of small
particles. This theory was founded in ancient times by Democritus and
expressed in poetic form by Lucretius. This view was challenged by the
opposite theory, according to which matter is a continuous expanse.
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