Period of a group
From Encyclopedia of Mathematics
The least common multiple of the orders of the elements in the group (it is assumed that the group is periodic and that the set of orders of all its elements is bounded). The period of a group is also called the exponent of the group.
Comments
The order of an element 
of a group 
is the least positive integer 
such that 
(where 
is the indentity of 
).
Cf. also Periodic group.
How to Cite This Entry:
Period of a group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Period_of_a_group&oldid=12557
Period of a group. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Period_of_a_group&oldid=12557
This article was adapted from an original article by O.A. Ivanova (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article