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I am wondering to know more about Baer groups and A-groups. I know their definition as below:

  • A Baer group is a group that all elements of prime power order have prime power index $[G:C_G(x)]$

  • An A-group is a group that all it's sylow subgroup are Abelian.

But I want to know more a bout them. For example are these groups always nilpotent? If someone introduses a book that can help me, I will really appreciate him/her.

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Are you talking about finite groups? If so, it would be helpful to say! – Derek Holt Jan 5 '13 at 10:01

Note that $S_3$ adheres to both of these properties and is not nilpotent. I believe Robinson has a good introduction to both of these topics.

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Thanks for your good tip. – Adeleh Jan 5 '13 at 16:45
Yes, the groups are finite. – Adeleh Jan 6 '13 at 9:38

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