Let G be a 2-group, and let Z(G) denote the equivariant cobordism algebra of G-manifolds with finite stationary point sets.A cobordism class in Z(G) is said to be indecomposable if it cannot be expressed as the sum of products of lower dimensional cobordism classes.Indecomposable classes generate the cobordism algebra Z(G). We discuss a sufficient criteria for indecomposability of cobordism classes. Using the above mentioned criterion, we show that the classes of Milnor manifolds (i.e., degree 1 hypersurfaces of the product of two real projective spaces) give non-trivial, indecomposable elements in Z(G) in degrees up to 2^n - 5. This talk is based on joint work with Samik Basu and Goutam Mukherjee.

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