Glauberman type not implies p-constrained
This article gives the statement and possibly, proof, of a non-implication relation between two group properties. That is, it states that every group satisfying the first group property (i.e., group of Glauberman type for a prime) need not satisfy the second group property (i.e., p-constrained group)
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Example of the special linear group
Further information: special linear group:SL(2,5), subgroup structure of special linear group:SL(2,5)
Let and . Then, is cyclic of order two, and is a simple group isomorphic to alternating group:A5. If is a -Sylow subgroup of , then is isomorphic to a quaternion group and , so . Thus, is not -constrained.
On the other hand, , so , so is of Glauberman type with respect to the prime .