Equation 677 Database

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Magma 12031464610d…

magma 12031464610d
Size
716
Isomorphism class hash
12031464610d7448026c0502484d0ba72c220c11293fc563da66a358454a795f
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 715) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 21:58:07
Display reorder
715,560,568,489,497,505,513,521,529,584,592,481,536,544,552,488,496,504,512,520,528,576,574,582,590,598,486,495,503,511,519,527,535,543,551,559,567,575,583,591,599,487,586,594,482,491,499,507,515,523,531,539,547,555,563,571,579,587,595,483,492,500,508,516,524,532,540,548,556,564,572,580,588,596,484,493,501,509,517,525,533,541,549,557,565,573,581,589,597,485,494,502,510,518,526,534,542,550,558,566,545,553,561,569,577,585,593,480,490,498,506,514,522,530,538,546,554,562,570,578,537,641,640,642,643,644,645,646,647,648,649,669,665,650,664,668,708,707,709,710,711,712,713,714,389,390,395,396,397,398,399,400,392,393,394,386,387,388,380,381,382,383,384,385,391,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,401,634,633,635,632,631,636,639,637,638,615,651,661,662,663,652,695,696,697,698,691,692,693,694,324,325,330,331,332,333,334,335,327,328,329,321,322,323,315,316,317,318,319,320,326,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,357,358,359,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,336,609,630,610,626,611,627,612,628,613,629,672,659,673,660,674,688,689,690,683,684,685,686,687,213,214,219,220,221,222,223,224,216,217,218,210,211,212,204,205,206,207,208,209,215,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,226,227,228,229,230,231,232,233,234,235,236,237,238,239,120,121,122,123,124,125,225,618,601,619,620,621,602,603,617,616,600,670,653,654,655,671,699,706,702,703,704,705,700,701,119,1,5,6,7,8,9,10,2,3,4,116,117,118,110,111,112,113,114,115,0,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,11,604,622,605,623,606,624,607,625,608,614,666,656,657,658,667,680,681,682,676,675,677,678,679 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 716 = 1 + 5*143, 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#d06be46a512d7443c089bc3030f3df281c845eba3c792e70152c014fa0d535cd, M = {143} 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, 143): MacNeish's product over GF(11) x GF(13); 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: 1.

last edited by qawbecrdtey at 2026-10-03 21:58:08 · history