Based on Cohn and Umans’ group-theoretic method, we embed matrix multiplication into several group algebras, including those of cyclic groups, dihedral groups, special linear groups and Frobenius groups. We prove that SL2(Fp) and PSL2(Fp) can realize the matrix tensor ⟨p, p, p⟩, i.e. it is possible to encode p × p matrix multiplication in the group algebra of such a group. We also find the lower bound for the order of an abelian group realizing ⟨n, n, n⟩ is n3. For Frobenius groups of the form Cq Cp, where p and q are primes, we find that the smallest admissible value of q must be in the range p4/3 ≤ q ≤ p2 − 2p + 3. We also develop an algorithm to find the smallest q for a given prime p.

Creator

• Li, Zimu

Contributors

• Cathain, Padraig O

Degree

• MS

Unit

• Mathematical Sciences

Publisher

• Worcester Polytechnic Institute

Language

• English

Identifier

• etd-012318-234642

Keyword

• Frobenius group
• special linear group
• fast matrix multiplication
• group-theoretic method
• cyclic group
• dihedral group
• representation theory

Advisor

• Cathain, Padraig O

Defense date

• 2017-11-28

Year

• 2018

Date created

• 2018-01-23

Resource type

• Thesis

Rights statement

• In Copyright