Subsocles Supporting Isotype and Balanced Subgroups
Canadian mathematical bulletin, Tome 36 (1993) no. 4, pp. 419-425
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We identify a condition, which we refer to as cohesiveness, on a subgroup S of the socle G[p] — {x ∊ G : px = 0} of an abelian p-group G which is necessary for S to be the socle of an isotype subgroup of G. It is shown, when S is countable, that this condition is both necessary and sufficient. A further restriction, definable in terms of the coset valuation on G/S, leads to the notion of S being completely cohesive in G. When S is countable, this latter condition is both necessary and sufficient for S to serve as the socle of a balanced subgroup of G. Also noteworthy is the fact that if H and K are, respectively, balanced and isotype subgroups of G with H[p] = K[p], then K is necessarily balanced in G.
Hill, Paul; Megibben, Charles. Subsocles Supporting Isotype and Balanced Subgroups. Canadian mathematical bulletin, Tome 36 (1993) no. 4, pp. 419-425. doi: 10.4153/CMB-1993-057-x
@article{10_4153_CMB_1993_057_x,
author = {Hill, Paul and Megibben, Charles},
title = {Subsocles {Supporting} {Isotype} and {Balanced} {Subgroups}},
journal = {Canadian mathematical bulletin},
pages = {419--425},
year = {1993},
volume = {36},
number = {4},
doi = {10.4153/CMB-1993-057-x},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-057-x/}
}
TY - JOUR AU - Hill, Paul AU - Megibben, Charles TI - Subsocles Supporting Isotype and Balanced Subgroups JO - Canadian mathematical bulletin PY - 1993 SP - 419 EP - 425 VL - 36 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-057-x/ DO - 10.4153/CMB-1993-057-x ID - 10_4153_CMB_1993_057_x ER -
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