Groups of order p^8 and exponent p
We prove that for p>7 there are p^4 +2p^3 +20p^2 +147p+(3p+29)gcd(p−1,3)+5gcd(p−1,4)+1246 groups of order p^8 with exponent p. If P is a group of order p^8 and exponent p, and if P has class c>1 then P is a descendant of P/γ c (P). For each group of exponent p with o...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2015-12-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | http://www.theoryofgroups.ir/pdf_5758_388335a7f7fa07bfe83e3a007db2f69c.html |
| Summary: | We prove that for p>7 there are
p^4 +2p^3 +20p^2 +147p+(3p+29)gcd(p−1,3)+5gcd(p−1,4)+1246
groups of order p^8 with exponent p. If P is a group of order p^8
and exponent p, and if P has class c>1 then P is a descendant of P/γ c (P). For each group of exponent p with order less than p^8 we calculate the number of descendants of order p^8 with
exponent p. In all but one case we are able to obtain a complete and irredundant list of the descendants. But in the case of the three generator class two group of order p^6 and exponent p (p>3 ), while we are able to calculate the number of descendants of order p^8, we have not been able to obtain a list of the descendants. |
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| ISSN: | 2251-7650 2251-7669 |