Equation 677 Database

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Magma 385cd39c1485…

magma 385cd39c1485
Size
707
Isomorphism class hash
385cd39c1485748b483bee4f6d790cc4b5d99efb78bd8d794eff67279f457f2b
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 05:06:38
Display reorder
302,300,301,304,305,303,656,212,211,210,215,213,214,175,174,176,179,177,178,154,153,155,150,151,152,253,254,252,255,256,257,120,122,121,125,123,124,2,0,1,3,4,5,131,130,129,127,128,126,133,132,134,137,135,136,159,161,160,156,157,158,184,183,185,180,181,182,464,463,465,466,467,462,500,499,501,502,503,498,525,524,526,527,522,523,450,455,451,452,453,454,600,601,602,603,604,605,474,479,475,476,477,478,468,473,469,470,471,472,494,493,495,496,497,492,484,483,485,480,481,482,398,397,399,400,401,396,624,610,621,608,607,628,635,639,622,630,677,670,671,683,706,676,693,685,674,691,68,67,66,71,69,70,64,63,65,62,60,61,41,40,39,36,38,37,266,264,265,268,269,267,108,110,109,113,111,112,54,56,55,58,59,57,224,223,222,226,227,225,271,272,270,274,275,273,208,207,209,205,206,204,292,291,293,288,289,290,420,425,421,422,423,424,584,583,585,586,587,582,574,573,575,570,571,572,562,561,563,558,559,560,506,505,507,508,509,504,356,355,357,358,359,354,517,516,518,519,520,521,598,597,599,595,594,596,360,365,361,362,363,364,393,392,394,395,390,391,648,646,651,637,643,649,632,640,620,631,695,703,697,659,705,678,704,699,698,692,162,164,163,165,166,167,44,43,42,45,46,47,105,107,106,104,102,103,22,21,23,18,19,20,51,53,52,50,48,49,217,216,218,221,219,220,281,280,279,276,278,277,144,146,145,148,149,147,200,199,198,203,201,202,296,295,294,298,299,297,337,336,338,339,340,341,386,385,387,388,389,384,351,350,352,353,348,349,590,589,591,592,593,588,436,435,437,432,433,434,445,444,446,447,448,449,514,513,515,510,511,512,486,491,487,488,489,490,346,345,347,342,343,344,406,405,407,402,403,404,650,644,655,636,642,654,615,641,616,629,696,701,700,673,689,672,688,690,687,675,258,259,260,262,263,261,83,82,81,79,78,80,231,233,232,230,228,229,242,241,240,244,245,243,193,192,194,195,196,197,74,72,73,75,76,77,26,25,24,28,29,27,114,116,115,118,119,117,7,6,8,10,11,9,282,283,284,285,286,287,528,533,529,530,531,532,326,325,327,328,329,324,566,565,567,568,569,564,370,369,371,366,367,368,545,544,540,541,542,543,547,546,548,549,550,551,577,576,578,579,580,581,414,419,415,416,417,418,409,408,410,411,412,413,306,307,308,309,310,311,652,645,647,633,634,653,617,638,623,618,702,686,684,658,681,679,694,682,680,657,87,89,88,84,85,86,172,171,173,170,168,169,98,97,96,100,101,99,94,93,95,90,91,92,251,250,249,246,248,247,17,16,15,12,13,14,234,236,235,239,237,238,190,189,191,188,186,187,33,35,34,30,31,32,139,138,140,141,142,143,381,380,382,383,378,379,322,321,323,318,319,320,376,375,377,372,373,374,556,555,557,552,553,554,330,335,331,332,333,334,313,312,314,315,316,317,461,460,456,457,458,459,429,428,430,431,426,427,438,443,439,440,441,442,534,539,535,536,537,538,619,613,626,606,609,625,614,627,611,612,669,661,668,665,662,663,667,664,660,666 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#f44078deebe7730562c927e2829a32c42b90cd1087b6200dbe445a4d4d2f9fa6, M = {18, 19, 20, 21, 22, 23, 130} 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 05:06:44 · history