Project A MATH GROUPIE

Group theory is a division of abstract algebra. Groups are fundamental to mathematics — "they're essentially the building blocks on which the field is based," says Po-Ling. So what are some practical applications? Solving the Rubik's Cube is one. "The moves are an example of a mathematical group," she notes.

Her research has more meat, though. "My project involved special types of 'closed' groups and the mappings that arise between them," she explains. That has potential applications in cryptology and Internet security.

Want some details of her project? O.K., here goes: Group H is said to be a closed subgroup of a finite group G, provided any homomorphism of H into G extends uniquely to all of G.

Take the group D2p of symmetries of a regular polygon with p sides, where p is an odd prime number. If D2p is closed and properly contained inside a finite group G, then G must be complicated. In fact, Po-Ling proves that G cannot be solvable. She further conjectures that for any p greater than 3, there exist such G whose commutator subgroup is nonabelian finite simple.

To people like Po-Ling, stuff like that can be elegant beyond words. She quotes philosopher Bertrand Russell: "Mathematics, rightly viewed, possesses not only truth, but supreme beauty."


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INTEL SCIENCE SEARCH FINALIST Po-Ling Loh

Po-Ling Loh


Essay:

Curing Science's Gender Imbalance


James Madison Memorial High School
Madison, Wis.


Hobbies: Music, writing, history, cross-stitch needlework


Ambition: Math teacher or professor