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THE SUBGROUP COMMUTATIVITY DEGREE OF FINITE
$P$-GROUPS
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 93 / Issue 1 / February 2016
- Published online by Cambridge University Press:
- 08 July 2015, pp. 37-41
- Print publication:
- February 2016
-
- Article
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The subgroup commutativity degree of a group
$G$ is the probability that two subgroups of 
$G$ commute, or equivalently that the product of two subgroups is again a subgroup. For the dihedral, quasi-dihedral and generalised quaternion groups (all of 2-power cardinality), the subgroup commutativity degree tends to 0 as the size of the group tends to infinity. This also holds for the family of projective special linear groups over fields of even characteristic and for the family of the simple Suzuki groups. In this short note, we show that the family of finite 
$P$-groups also has this property.
