Equation 677 Database

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Magma 25db1f0f6933…

magma 25db1f0f6933
Size
707
Isomorphism class hash
25db1f0f6933184ff5dcb9f899de68b29ea475883837ef1a407663a213454873
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 706) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 14:26:54
Display reorder
134,133,135,136,137,132,706,291,290,292,293,288,289,221,216,217,219,220,218,241,245,240,242,243,244,237,236,238,239,235,234,222,223,224,225,226,227,92,91,93,94,95,90,13,12,14,15,16,17,1,5,0,2,3,4,301,305,300,302,303,304,298,299,294,296,297,295,390,392,391,393,394,395,405,407,406,403,404,402,512,511,510,513,514,515,397,396,398,399,400,401,539,538,537,536,535,534,441,443,442,440,438,439,450,452,451,455,453,454,343,342,344,346,347,345,500,499,498,502,503,501,422,421,420,424,425,423,608,610,612,609,607,606,640,629,641,638,700,678,698,683,699,690,691,704,705,703,70,69,71,66,67,68,170,172,171,168,169,173,233,232,229,228,230,231,78,83,79,80,81,82,28,27,29,24,25,26,148,147,149,144,145,146,49,48,50,51,52,53,124,123,125,120,121,122,207,206,208,209,204,205,6,11,7,8,9,10,369,371,370,366,367,368,314,313,312,315,316,317,552,553,554,557,555,556,550,549,551,547,546,548,474,476,475,477,478,479,483,485,484,482,480,481,489,491,490,488,486,487,466,465,467,463,464,462,322,321,323,318,319,320,543,544,540,541,542,545,620,619,618,615,616,613,614,617,611,637,701,689,702,663,673,672,674,679,684,685,159,158,160,161,156,157,23,19,18,21,22,20,174,179,175,176,177,178,259,263,258,260,261,262,163,162,164,165,166,167,264,269,265,266,267,268,30,35,31,32,33,34,150,155,151,152,153,154,281,280,277,276,278,279,86,85,87,88,89,84,565,566,564,567,568,569,360,362,361,364,365,363,561,563,562,558,560,559,574,573,575,571,570,572,427,426,428,430,431,429,375,377,376,374,372,373,496,495,497,492,493,494,382,381,383,379,380,378,437,436,435,433,434,432,456,458,457,461,459,460,635,632,621,633,630,634,642,631,639,636,693,692,694,669,668,680,664,686,681,695,282,283,284,285,286,287,44,46,45,42,43,47,271,270,275,272,274,273,56,55,57,58,59,54,211,210,212,213,214,215,130,129,131,126,127,128,139,138,140,141,142,143,40,39,41,36,37,38,64,63,65,60,61,62,74,73,75,76,77,72,359,358,357,356,354,355,601,602,600,604,605,603,310,309,311,308,307,306,349,348,350,351,352,353,581,580,579,578,577,576,324,326,325,329,327,328,585,587,586,584,583,582,595,596,594,597,598,599,470,469,468,472,473,471,589,590,588,593,591,592,647,644,648,645,646,643,651,653,650,654,696,677,697,670,675,676,667,688,682,687,103,102,104,105,106,107,194,196,195,192,193,197,115,114,116,117,118,119,181,180,182,183,184,185,113,112,108,109,110,111,248,251,247,250,249,246,203,202,198,199,200,201,101,100,96,97,98,99,257,256,253,252,254,255,191,190,186,187,188,189,330,332,331,333,334,335,532,531,533,530,528,529,524,523,522,525,526,527,338,337,336,340,341,339,519,521,520,516,517,518,447,449,448,446,444,445,504,506,505,509,507,508,415,414,416,418,419,417,388,387,389,384,385,386,412,411,413,408,409,410,628,649,627,625,626,622,652,624,623,655,666,660,665,658,657,659,656,661,662,671 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 707 = 7 + 5*140, 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#20e9cec11ce1b4ef3a4be2ce0eb77a027f26009c155c08499f343b203c8ba1b3, M = {36, 37, 38, 39, 40, 41, 138} 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, 140): MacNeish's product over GF(4) x GF(5) x GF(7); 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: 101.

last edited by qawbecrdtey at 2026-10-08 14:26:55 · history