Vol. 53, No. 1, 1974

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The non-minimality of induced central representations

David Lee Wright

Vol. 53 (1974), No. 1, 301–306

Let G be a finite p-group and G a minimal faithful permutation representation of G possessing the minimal number of generators of the centre of G transitive constituents. One surmises that the induced representation, G, of the centre of G, is minimal. The conjecture is validated subject to either of the hypotheses |G|pf except G = Q8 × Z1 or Z(G)n copies of the cyclic group of order pm and is trivial when G is abelian. However, a group of order p6 shows the conjecture to be false for p odd, also. The converse problem of extending minimal representations of Z(G) to minimal representations of G is also, in general, not possible.

Mathematical Subject Classification 2000
Primary: 20C15
Received: 12 June 1973
Published: 1 July 1974
David Lee Wright