The number of different orders of nonidentity elements in a group is limited by the number divisors of the order of the group. This upper bound can be made more specific for proper subgroups, and can be calculated from the prime power factorization of the group's order. Some groups have subgroups with the highest possible number of different orders for nonidentity elements. This property can be characterized and general results exist for several families of groups.

Author Bio

Iordan Ganev is a Bulgarian-American attending Miami University as part of the class of 2010. He is pursuing a Bachelor of Science degree in mathematics and statistics and a second major in environmental science. During his junior year, Iordan will be studying in London. Upon graduation, he plans to obtain a doctorate in mathematics. Iordan enjoys music, travel, archeology, and mountain hiking.