群的直积的检验元素

潘江敏. 群的直积的检验元素[J]. 云南大学学报(自然科学版), 2005, 27(1): 5-8.

引用本文:

潘江敏. 群的直积的检验元素[J]. 云南大学学报(自然科学版), 2005, 27(1): 5-8.

PAN Jiang-min. On test elements of direct products of groups[J]. Journal of Yunnan University: Natural Sciences Edition, 2005, 27(1): 5-8.

Citation:

PAN Jiang-min. On test elements of direct products of groups[J]. Journal of Yunnan University: Natural Sciences Edition, 2005, 27(1): 5-8.

On test elements of direct products of groups

摘要: 群G的一个元素g称为G的检验元素,如果G的每一个保持g不变的自同态都是G的自同构.本文讨论了群的直积的检验元素的一些性质.作为应用,给出了任意阿贝尔群有检验元素的充分必要条件,并确定了其检验元素.

Abstract: An element g is a test element of a group G if every homomorphism of G which keeps g fixed is an automorphism.Some properties of test elements of direct products of groups are verified.Moreover,a necessary and sufficientcondition for an abelian group to have test elements is specified.Also,the test elements are determined.

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