We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 07 September 2010
INTRODUCTION
It has been known for some time [1, Ch.18] that finitely generated groups of exponent 2, 3, 4 or 6 are finite. So far there is much less known on groups of exponent 5. It was shown by Kostrikin in 1955 that the largest finite group with two generators has order at most 534. In 1956 Graham Higman used a combinatorial argument to show that for any finite number of generators there is a largest finite group of exponent 5. In 1974 Havas, Wall and Warns ley showed that the largest finite two generator group of exponent 5 has order exactly 534 and they found a detailed table of commutator relations which describe this group exactly.
In this paper in an attempt to prove finite B(5,2) the Burnside group of exponent 5 with two generators, it is shown that B(5,2) has a normal subgroup K1 of index 510. K1 is the normal closure of 24 explicit elements. K1 should be an Abelian group of order 524. This reduces the proof of the finiteness of B(5,2) to a proof that K1 is Abelian.
To save this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
