  Although recent advances of blockchain systems, notably in the form of
cryptocurrency, have drawn tremendous interests from both researchers and
practitioners, limited studies existed toward the theoretical foundation of
blockchains. This paper presents the first study on the algebraic structure of
blockchains with an emphasis on the internal properties under algebraic groups.
We axiomatically construct a blockchain group and derive some interesting
properties that can be potentially taken into the design space and parametric
analysis of real-world blockchain systems.
