Equation 677 Database

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Magma 716c42315592…

magma 716c42315592
Size
707
Isomorphism class hash
716c42315592ef2f14d3e97983778777b14256a8ca16f5631fb9a3f8ccb68cc4
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 01:39:04
Display reorder
287,286,285,283,282,284,644,76,75,77,73,74,72,128,127,126,129,130,131,65,64,63,61,62,60,123,125,124,122,120,121,268,267,269,265,264,266,160,159,161,156,157,158,7,6,8,11,9,10,150,152,151,155,153,154,299,298,297,296,295,294,137,136,135,133,134,132,408,407,409,404,405,406,345,344,346,347,342,343,489,488,490,491,492,493,560,559,561,562,563,558,341,340,336,337,338,339,557,556,553,552,554,555,592,591,593,588,589,590,551,550,546,547,548,549,374,373,375,376,377,372,600,605,601,602,603,604,616,609,627,607,628,619,632,640,621,630,682,687,705,679,706,685,689,684,677,688,272,270,271,275,273,274,221,220,219,217,216,218,213,215,214,212,211,210,223,224,222,227,225,226,206,204,205,208,209,207,93,95,94,92,90,91,88,87,89,86,84,85,261,263,262,260,259,258,239,238,237,236,234,235,81,83,82,80,78,79,520,519,521,522,523,518,355,354,356,357,358,359,494,499,495,496,497,498,529,528,525,524,526,527,310,309,311,307,306,308,533,532,534,535,530,531,570,575,571,572,573,574,464,469,465,466,467,468,362,361,363,364,365,360,418,417,419,420,421,416,648,642,654,638,649,655,636,635,617,631,680,678,692,657,658,673,672,663,662,659,280,279,281,276,278,277,26,25,24,27,28,29,245,244,243,240,242,241,21,23,22,20,18,19,163,164,162,165,166,167,35,34,33,31,32,30,67,66,68,71,69,70,201,203,202,200,198,199,41,40,39,38,36,37,182,181,180,184,185,183,458,463,459,460,461,462,410,415,411,412,413,414,481,480,476,477,478,479,321,320,322,323,318,319,316,315,317,312,313,314,580,579,581,576,577,578,440,445,441,442,443,444,484,483,485,486,487,482,500,505,501,502,503,504,510,509,511,506,507,508,650,643,653,639,646,656,626,633,625,622,674,676,675,670,664,661,690,669,667,694,188,187,186,191,189,190,172,171,173,170,168,169,252,253,254,255,256,257,114,116,115,119,117,118,141,143,142,140,138,139,112,111,113,108,109,110,3,5,4,0,2,1,250,249,251,247,246,248,233,232,231,230,229,228,44,43,42,46,47,45,475,474,470,471,472,473,368,367,369,370,371,366,537,536,538,539,540,541,403,402,542,545,543,544,435,434,436,437,438,439,433,432,428,429,430,431,427,426,422,423,424,425,564,569,565,566,567,568,515,514,516,517,512,513,351,350,352,353,348,349,651,641,652,637,645,647,623,634,624,613,681,683,686,666,665,668,671,691,693,660,56,55,54,59,57,58,12,14,13,16,17,15,288,289,290,291,292,293,147,149,148,146,144,145,52,51,53,48,49,50,101,100,99,97,98,96,175,174,176,179,177,178,103,102,104,105,106,107,300,302,301,303,304,305,194,193,192,196,197,195,457,456,452,453,454,455,332,331,333,334,335,330,327,326,328,329,324,325,399,398,400,401,396,397,395,394,390,391,392,393,388,387,389,384,385,386,586,585,587,583,582,584,451,450,446,447,448,449,382,381,383,378,379,380,599,598,594,595,596,597,629,611,618,606,620,615,612,614,608,610,695,702,703,696,704,699,697,700,701,698 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 = {48, 49, 50, 51, 52, 53, 131} 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 01:39:05 · history