Groups of order 91

This article gives information about, and links to more details on, groups of order 91
See pages on algebraic structures of order 91 | See pages on groups of a particular order

Up to isomorphism, there is a unique group of order 91, namely cyclic group:Z91, which is also the external direct product of cyclic group:Z7 and cyclic group:Z13.

The fact of uniqueness follows from the classification of groups of order a product of two distinct primes. Since $91=7\cdot 13$ and $7$ does not divide $(13-1)$, the number $91$ falls in the one isomorphism class case.

Another way of viewing this is that $91$ is a cyclicity-forcing number, i.e., any group of order 91 is cyclic. See the classification of cyclicity-forcing numbers to see the necessary and sufficient condition for a natural number to be cyclicity-forcing.