Let p be a prime, G a locally finite p-group, K a commutative ring of characteristic p. The anti-automorphism g → g −1 of G extends linearly to an anti-automorphism a → a * of KG. An element a of KG is called symmetric if a * = a. In this paper we answer the question: for which G and K do the symmetric units of KG form a multiplicative group. Let G be a group, K a commutative ring (with 1), and U (KG) the group of units in the group algebra KG. The anti-automorphism g → g −1 of G extends linearly to an anti-automorphism a → a * of KG ; this extension leaves U (KG) setwise invariant. An element a of KG is called symmetric if a * = a.

In this paper, (1) we deduce a formula for the number of automorphism of finite Abelian p-group of rank two ( )

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