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Date: 2006-03-21 17:36:38 Quasinormal subgroup Abelian group Normal subgroup Index of a subgroup Solvable group P-group Subgroup Direct product of groups Commutator subgroup Abstract algebra Group theory Algebra		Add to Reading List Source URL: www.maths.tcd.ie Download Document from Source Website File Size: 156,75 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