N23a Easter 2008 NATURAL SCIENCES TRIPOS PART IB

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Date: 2008-04-21 17:12:43 Group theory Quotient group Coset Subgroup Normal subgroup Group Cyclic group Permutation Matrix Abstract algebra Algebra Mathematics		N23a Easter 2008 NATURAL SCIENCES TRIPOS PART IB Add to Reading List Source URL: www.atm.damtp.cam.ac.uk Download Document from Source Website File Size: 42,37 KB Share Document on Facebook

	THE SCHUR–ZASSENHAUS THEOREM KEITH CONRAD When N is a normal subgroup of G, can we reconstruct G from N and G/N ? In general, no. For instance, the groups Z/(p2 ) and Z/(p) × Z/(p) (for prime p) are nonisomorphic, but DocID: 1vr1L - View Document
	SUBGROUP SERIES I KEITH CONRAD 1. Introduction If N is a nontrivial proper normal subgroup of a finite group G then N and G/N are smaller than G. While it is false that G can be completely reconstructed from knowledge DocID: 1v04a - View Document
	SUBGROUP SERIES II KEITH CONRAD 1. Introduction In part I, we met nilpotent and solvable groups, defined in terms of normal series. Recalling the definitions, a group G is called nilpotent if it admits a normal series (1 DocID: 1ucTI - View Document
	HomeworkFind a normal subgroup of S4 of orderShow that a group of order 385 is solvable. 3. Write (x2 + y 2 )(x2 + z 2 )(y 2 + z 2 ) DocID: 1t5ke - View Document
	Restricting representations to a normal subgroup - Compact Quantum Groups Alfried Krupp Wissenschaftskolleg Greifswald DocID: 1sCOp - View Document