Equation 677 Database

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Magma 1f527dc604a4…

magma 1f527dc604a4
Size
381
Isomorphism class hash
1f527dc604a464816be29e54bacb25103c73ae8b114710dbe8ed188327c40f60
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:34:37
Display reorder
380,257,92,87,77,82,70,212,217,222,198,203,207,8,9,7,19,186,260,265,271,276,281,295,140,145,150,126,131,136,301,300,302,303,304,4,5,192,20,21,287,180,171,176,165,156,291,45,50,55,60,66,227,232,236,240,245,250,96,101,109,110,115,305,6,160,120,336,355,330,366,346,361,376,342,350,372,258,93,88,78,83,73,214,219,224,199,204,209,37,38,36,40,189,261,266,270,277,282,297,142,147,152,127,132,137,325,326,324,328,329,41,42,194,43,44,289,184,174,179,169,159,293,48,53,58,63,68,229,234,239,244,249,254,97,102,106,112,117,327,39,164,122,339,359,333,367,348,362,378,344,352,374,259,94,89,79,84,74,210,215,220,197,202,206,15,16,14,18,185,264,269,274,279,284,299,144,149,154,129,134,139,310,311,309,307,308,1,0,190,2,3,286,181,170,175,166,155,294,49,54,59,64,69,226,231,235,241,246,251,99,104,108,114,119,306,17,161,124,335,356,331,369,349,363,379,340,354,370,256,90,85,76,81,71,213,218,223,195,200,208,27,28,29,30,188,262,267,272,275,280,296,141,146,151,125,130,135,312,313,314,315,316,35,32,193,33,34,288,183,173,178,168,158,290,46,51,56,61,65,225,230,237,242,247,252,95,100,105,111,116,317,31,163,121,338,357,334,365,345,360,375,343,351,373,255,91,86,75,80,72,211,216,221,196,201,205,22,23,24,25,187,263,268,273,278,283,298,143,148,153,128,133,138,318,319,320,321,322,10,11,191,12,13,285,182,172,177,167,157,292,47,52,57,62,67,228,233,238,243,248,253,98,103,107,113,118,323,26,162,123,337,358,332,368,347,364,377,341,353,371 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#890900158510c31f70f4fa8bc84bbffcea5cd35bea72b3996f708723e8ad424c, M = {69} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-01 23:34:38 · history