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1978•Canadian Journal of MathematicsOpen access

Non-Isomorphic Burnside Groups of Exponent p 2

Kenneth Keller Hickin, Richard E. Phillips

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Abstract

In the recent paper [8] Phillips has shown that for each prime p there are 2 ℵ0 non-isomorphic 2-generatecl p-groups. This same result was obtained independently by S. Jeanes and J. S, Wilson (unpublished) who show that the groups constructed in [1] have 2 ℵ0 non-isomorphic images. The groups in both of these proofs all have infinite exponent. In this paper we show that, for large enough primes p, there are 2 ℵ0 non-isomorphic 2-generated groups of exponent p2.

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What this paper is about

In the recent paper [8] Phillips has shown that for each prime p there are 2 ℵ0 non-isomorphic 2-generatecl p-groups. This same result was obtained independently by S. Jeanes and J. S, Wilson (unpublished) who show that the groups constructed in [1] have 2 ℵ0 non-isomorphic images. The groups in both of these proofs all have infinite exponent. In this paper we show that, for large enough primes p, there are 2 ℵ0 non-isomorphic 2-generated groups of exponent p2.

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Available abstract

In the recent paper [8] Phillips has shown that for each prime p there are 2 ℵ0 non-isomorphic 2-generatecl p-groups. This same result was obtained independently by S. Jeanes and J. S, Wilson (unpublished) who show that the groups constructed in [1] have 2 ℵ0 non-isomorphic images. The groups in both of these proofs all have infinite exponent. In this paper we show that, for large enough primes p, there are 2 ℵ0 non-isomorphic 2-generated groups of exponent p2.

Key concepts: Mathematics, Exponent, Mathematical proof, Combinatorics, Prime (order theory), Pure mathematics, Discrete mathematics, Geometry

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