## On Locally Compact Totally Disconnected Abelian Groups and Their Character Groups |

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Abelian p-primary group arbitrarily small subgroups arbitrary neighborhood auxiliary group bicontinuous canpact CHARACTER THEORY clearly a homomorphism compact p-primary group compact set compact subset compact T.D.A. group continuous homomorphism Corollary cyclic group Define discrete group discrete topology duality theory element of H elements of infinite f is continuous finite groups finite number finite order follows G into g G is compact G is discrete G is L.C.A. G is p-primary given group G groups isomorphic Hence homomorphism of G infinite height L.C.A. group L.C.A. p-primary groups L.C.T.D.A. groups Lemma Let G locally compact neighborhood in G non-zero normal subgroup open compact subgroup open in G open subgroup p-adic integers p-group partially ordered set permutation matrices Pontrjagin primary components Proof Proposition qn,x separated topology subgroup H subgroup of G sufficiently many representations Theorem 3.3 topological group Zp,g