#### Volume 10, issue 4 (2010)

The beta elements $\beta_{tp^2/r}$ in the homotopy of spheres
 1 H R Miller, D C Ravenel, W S Wilson, Periodic phenomena in the Adams–Novikov spectral sequence, Ann. Math. $(2)$ 106 (1977) 469 MR0458423 2 S Oka, A new family in the stable homotopy groups of spheres, Hiroshima Math. J. 5 (1975) 87 MR0380791 3 S Oka, A new family in the stable homotopy groups of spheres. II, Hiroshima Math. J. 6 (1976) 331 MR0418096 4 S Oka, Realizing some cyclic $\mathrm{BP}_{*}$–modules and applications to stable homotopy of spheres, Hiroshima Math. J. 7 (1977) 427 MR0474290 5 D C Ravenel, Complex cobordism and stable homotopy groups of spheres, AMS Chelsea Publ. 347, Amer. Math. Soc. (2004) MR860042 6 K Shimomura, Note on beta elements in homotopy, and an application to the prime three case, Proc. Amer. Math. Soc. 138 (2010) 1495 MR2578544 7 L Smith, On realizing complex bordism modules. IV. Applications to the stable homotopy groups of spheres, Amer. J. Math. 99 (1977) 418 MR0433450 8 N Yamamoto, Algebra of stable homotopy of Moore space, J. Math. Osaka City Univ. 14 (1963) 45 MR0157382