Group of prime power order in which every maximal subgroup is isomorph-free
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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- Any cyclic group of prime power order satisfies this property. In fact, a cyclic group of prime power order has a unique maximal subgroup, which has order and equals the first agemo subgroup, i.e., the set of powers.
- Among the non-cyclic groups of prime power order, the smallest example of one in which every maximal subgroup is isomorph-free is the semidihedral group of order sixteen (also see subgroup structure of semidihedral group:SD16. This is a group of order having three maximal subgroups of order : a cyclic group, dihedral group and quaternion group.
Relation with other properties
- Group of prime power order in which every maximal subgroup is characteristic
- Group in which every maximal subgroup is characteristic