The security of telecommunication largely depends on effective and safe coding. National security as well as the safety of the entire society also depends on how information is exchanged between government agencies. The security of information can also be guaranteed by a safe and effective coding system. A Hamming code is a linear error-correcting code which can detect and correct single-bit errors. It can also detect, but not correct up to two simultaneous bit errors. For each integer m > 1 there is a code with the parameters {2m−1, 2m−m−1, 3}. The factorization of Abelian groups and the complete factor problem of 2-groups are closely related to the error-correcting Hamming codes. In this paper we will deal with the Rédei property of 2-groups.