66th Annual STS (2006-2007)
Finalists
Brian Robert Lawrence
MARYLAND
Brian Robert Lawrence, 17, of Kensington, involved classical matrix groups
with the classification theorem of finite simple groups for his Intel Science
Talent Search in mathematics. He classifies several families of minimal finite
groups, such as the smallest ones with exactly
p2 - 1 elements of order p for any prime p.
A finite group G occurs as a
nonempty subset of all permutations of some fixed finite set X which is closed
under taking inverses and compositions. The order of an element g of G is the
least positive integer such that gn is the identity map on X. Brian lists
examples of minimal groups, proves a bound on the possible size that any example
could have, and then shows that his list is complete.
Brian attends Montgomery Blair High School in Silver Spring, where he is captain
of the math team. He has earned national and international mathematical honors
and independently studies Latin and Chinese. Principal cellist in the Maryland
Classic Youth Orchestra, Brian also enjoys playing in the American Youth
Philharmonic. The son of Drs. James and Vivian Lawrence, he plans to pursue a
career as a mathematician because of "the beauty and structure of the subject."
