Free subgroups of small cancellation groups |
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Authors: | Mohamed S El-Mosalamy |
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Institution: | (1) Department of Mathematics, Glasgow University, G12 8QW Glasgow, Scotland, U.K. |
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Abstract: | In this paper we give a simple proof of Collin’s theorem concerning free subgroups ofC(4),T(4) groups. Our proof actually shows that a slenderT(4) presentation 〈x
1,x
2, …,x
n
;r〉 has a free subgroup of rank 2 provided there is a subset {a, b, c} of {x
1,x
2, …,x
n
} with the property that any non-empty freely reduced word ina, b, c equal to 1 inG has a subword of length 2 contained in an element ofr*. |
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Keywords: | |
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