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seminars:alge

Evariste Galois Emmy Noether

The Algebra Seminar

Unless stated otherwise, the seminar meets Tuesdays in room WH-100E at 2:50 p.m. There will be refreshments served at 4:00 in room WH-102.

Organizers: Ben Brewster and Fernando Guzmán

To receive announcements of seminar talks by email, please join the seminar's mailing list.


Spring 2017

  • January 24
    Ben Brewster (Binghamton University)
    The Frattini subgroup

    Abstract: The Frattini subgroup of group G (denoted Fr G ) is defined as the intersection of all the maximal subgroups of G. If G has no maximal subgroups, the standard device is that G = Fr G. This talk will be concerned primarily with non-trivial finite groups and so this standard device is not relevant.

    • The Frattini subgroup is called by the name of its originator in 1885. It is analogous to the Jacobson radical in ring theory and it can be generalized to various posets.
    • I will present some examples and basic results about the Frattini subgroup. It has many different uses in Group theory. I will choose a few and give some examples, but then tackle the question of which groups G can be Fr H for some H.
    • Speaking now about finite groups, it turns out the Frattini subgroup is nilpotent, every finite abelian group is isomorphic to the Frattini subgroup of an abelian group, but no non-abelian group of order p^3 is isomorphic to the Frattini subgroup of any group.
    • I am unaware of the classification of groups G such that G is isomorphic to Fr H for some H.
  • January 31
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  • February 07
    Matt Evans (Binghamton University)
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  • February 14
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  • February 21
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  • February 28
    Joe Cyr (Binghamton University)
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  • March 07

    Winter Break

  • March 14
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  • March 21
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  • March 28
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  • April 04
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  • April 11

    Spring Break

  • April 18
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  • April 25
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  • May 02
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seminars/alge.txt · Last modified: 2017/01/19 15:29 by ben