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Özgün Ünlü

On Ranks for Finite Supersolvable Groups and Actions on Products of Spheres

We give counter-examples to [5, Conjecture 1.1]. Example 1 is a 2-group G of order 128 for which axe(G) = 3 and saw(G) = 4. In Example 2, for p, q prime numbers with q ? 1 mod p, we give a supersolvable group G_pq of order p²q^p+1 with axe(G_pq) = p + 1 and saw(G_pq = p + 2. Our smallest example has of order 108 = 2²3²⁺¹ and all of our examples are minimal in the sense that they have no proper subgroup with unequal axe and saw rank.

Journal of Group Theory, Walter de Gruyter

Print ISSN: 1433-5883
Volume: 8, 01/2005
Pages: 109 - 113

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