Equation 677 Database

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Magma a3c57969ac28…

magma a3c57969ac28
Size
707
Isomorphism class hash
a3c57969ac284a7cb554a40b8f815a40d5a1409f44511b0d2159aa77a90642f7
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
2026-10-09 00:52:56
Display reorder
138,143,139,140,141,142,706,42,45,43,44,41,40,137,136,132,133,134,135,47,46,48,49,50,51,288,293,289,290,291,292,62,61,63,64,65,60,38,37,39,34,35,36,257,256,252,253,254,255,299,298,294,295,296,297,300,305,301,302,303,304,282,283,284,285,286,287,468,467,469,466,464,465,516,515,517,513,514,512,578,577,576,579,580,581,314,313,312,315,316,317,387,389,388,391,390,527,484,483,482,487,485,486,587,586,585,584,583,582,542,541,540,525,526,524,368,367,366,364,365,363,309,311,310,307,306,308,609,610,607,612,611,608,635,632,630,636,694,695,674,686,705,699,704,702,703,693,191,194,192,193,190,195,189,188,184,185,186,187,246,245,247,248,249,244,124,123,125,120,121,122,10,9,11,6,7,8,17,16,12,13,14,15,4,3,5,1,0,2,221,220,222,223,224,225,27,26,22,23,24,25,179,178,180,181,182,183,419,421,420,417,418,416,351,353,352,348,349,350,436,435,434,437,438,439,440,442,441,444,445,443,345,347,346,344,342,343,431,433,432,428,429,430,425,427,426,422,423,424,339,341,340,336,337,338,507,506,508,509,510,511,369,371,370,372,373,374,614,615,618,616,613,617,629,619,628,627,697,701,671,669,690,676,696,679,688,672,90,93,91,92,95,94,97,96,98,99,100,101,86,85,87,88,89,84,158,157,159,160,161,156,130,129,131,126,127,128,106,105,107,102,103,104,216,215,217,218,219,214,213,212,208,209,210,211,201,200,196,197,198,199,54,53,55,56,57,52,572,570,571,573,574,575,356,355,354,544,545,543,537,539,538,535,536,534,327,329,328,325,326,324,529,528,530,531,532,533,412,411,410,415,413,414,548,547,546,551,549,550,361,360,362,358,359,357,501,500,502,503,504,505,333,335,334,330,331,332,625,620,624,606,622,623,634,633,626,631,683,700,664,665,675,689,685,682,677,678,150,153,151,152,155,154,21,20,251,19,18,250,243,242,238,239,240,241,234,233,235,236,237,232,229,228,230,231,226,227,108,113,109,110,111,112,176,175,177,172,173,174,205,204,206,207,202,203,145,144,146,147,148,149,118,117,119,114,115,116,554,553,552,555,556,557,561,563,562,558,559,560,519,518,520,523,521,522,375,377,376,379,380,378,452,454,453,457,455,456,593,592,591,590,589,588,595,596,594,597,598,599,600,601,602,604,605,603,450,449,451,446,447,448,462,461,463,459,460,458,647,646,648,650,649,621,639,640,638,637,691,698,668,666,681,680,684,692,687,673,81,170,82,83,80,79,72,78,73,169,74,75,271,275,270,272,273,274,31,30,32,33,28,29,262,261,263,258,260,259,163,162,164,165,166,171,77,58,70,71,167,59,276,277,278,279,280,281,266,264,267,268,269,265,76,69,168,66,67,68,405,404,406,409,407,408,491,493,492,488,489,490,481,480,479,476,477,478,567,569,568,565,566,564,393,392,394,395,396,397,386,385,384,383,381,382,318,320,319,321,322,323,474,473,475,471,472,470,497,499,498,496,494,495,403,402,401,400,398,399,651,652,655,654,653,644,645,641,642,643,661,667,656,657,662,660,670,663,659,658 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#d668bf04c36f8b4c67728650c5c82a046d470936a3c130394e60cdea0aa42f4e, M = {60, 61, 62, 63, 64, 65, 144} 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 2026-10-09 00:52:57 · history