Equation 677 Database

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Magma 04b24e9a4e59…

magma 04b24e9a4e59
Size
595
Isomorphism class hash
04b24e9a4e593e8980baa6145b1c9dd1d85e6b41b1a0bf533ed6bea1cc1d67ed
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 22:43:21
Display reorder
136,135,137,132,133,134,49,48,50,51,52,47,141,140,142,143,138,139,452,450,451,453,454,455,347,346,345,343,344,342,538,533,564,583,581,195,194,159,196,197,193,162,79,77,78,76,80,20,19,21,22,23,18,13,12,14,187,188,156,199,198,200,160,45,46,89,88,90,91,87,207,168,232,229,230,231,169,213,212,214,163,210,211,413,412,411,408,409,410,487,488,486,491,489,490,417,419,418,416,415,414,385,384,386,387,388,389,379,378,380,383,381,382,503,502,501,498,499,500,314,313,312,316,317,315,266,265,264,269,267,268,551,550,513,528,527,510,522,523,555,557,563,566,558,578,588,556,114,119,115,116,117,118,64,67,65,66,69,68,63,62,58,59,60,61,121,120,122,123,124,125,108,107,109,104,105,106,8,7,9,10,11,178,221,166,222,223,220,165,226,225,167,227,228,224,302,301,300,303,304,305,290,289,288,292,293,291,295,294,296,297,298,299,494,493,492,496,497,495,506,505,504,507,508,509,425,424,423,420,421,422,287,286,285,283,284,282,310,309,311,307,308,306,529,530,532,549,548,543,542,531,560,575,574,572,573,587,586,571,3,2,4,5,6,1,97,94,92,93,96,95,35,34,30,31,32,33,127,126,128,129,130,131,84,83,85,86,81,82,146,145,147,148,149,257,253,247,256,255,254,245,249,250,246,251,252,248,353,352,351,348,349,350,446,444,445,448,449,447,392,391,390,394,395,393,258,259,260,261,262,263,402,404,403,406,407,405,361,360,362,365,363,364,279,281,280,278,276,277,323,322,321,320,318,319,521,524,536,518,517,535,537,516,584,577,582,594,565,589,593,554,101,100,102,103,98,99,144,243,241,242,174,244,237,173,238,172,239,240,190,189,157,16,17,15,111,110,112,113,208,209,152,179,180,181,153,182,155,183,184,185,186,154,216,215,217,164,218,219,433,437,436,432,434,435,479,478,477,475,476,474,431,430,429,428,426,427,461,460,459,456,458,457,396,398,397,400,401,399,473,472,471,468,469,470,438,439,440,441,442,443,271,270,272,274,275,273,545,544,519,539,525,515,526,534,591,567,592,552,570,585,553,568,43,42,44,39,40,41,53,204,203,161,202,201,236,171,233,234,170,235,192,191,158,37,38,36,55,54,56,57,206,205,175,176,150,177,151,0,28,27,29,24,25,26,73,72,74,75,70,71,334,333,335,332,330,331,371,370,369,367,368,366,376,375,377,372,373,374,482,481,480,484,485,483,464,462,463,465,466,467,354,356,355,358,359,357,341,340,339,337,338,336,325,324,326,328,329,327,540,541,514,547,546,512,520,511,590,576,559,580,579,562,561,569 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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#96b028d3c6de0cbaff964417289f690895c6af42769867ad5a7d2affbed8a752, M = the submagma generated by {12, 24} (35 elements) 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, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-08 22:43:22 · history