Equation 677 Database

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Magma 09a3cd7d0b85…

magma 09a3cd7d0b85
Size
705
Isomorphism class hash
09a3cd7d0b85c5054a5aed37ee2cec902277285cf92a9758f039d1d1f44470e5
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 19:08:03
Display reorder
660,544,322,306,460,273,323,274,545,307,461,275,321,543,308,459,318,272,540,309,456,270,319,541,310,457,271,320,542,311,458,279,328,550,312,466,280,329,551,313,467,465,281,327,549,314,324,278,546,315,462,316,325,276,547,463,326,277,548,317,464,678,679,682,686,436,216,472,239,137,217,135,437,473,237,136,218,435,471,238,219,133,432,468,235,134,220,433,469,236,132,221,434,470,234,143,214,442,478,245,141,215,443,479,243,244,142,213,441,477,210,139,438,474,241,475,211,140,439,242,212,138,440,476,240,661,666,664,671,424,153,257,562,119,154,117,425,255,563,118,155,423,256,561,152,115,420,253,558,116,150,421,254,559,114,151,422,252,560,110,144,430,248,568,108,145,431,246,569,567,109,146,429,247,147,113,426,251,564,249,148,111,427,565,149,112,428,250,566,684,680,676,674,418,79,556,392,95,80,93,419,557,390,94,78,417,555,391,82,91,414,552,395,92,83,415,553,393,90,81,416,554,394,86,646,649,650,645,84,654,657,658,652,637,85,638,641,642,613,89,615,617,616,626,622,87,625,620,630,88,633,634,628,703,701,704,697,448,532,484,282,341,533,339,449,485,283,340,531,447,483,284,528,337,444,480,285,338,529,445,481,286,336,530,446,482,287,332,538,454,490,288,330,539,455,491,289,290,331,537,453,489,534,335,450,486,291,487,535,333,451,292,536,334,452,488,293,689,692,691,694,67,406,19,382,159,407,160,68,20,383,161,405,66,18,381,402,158,70,22,378,156,403,71,23,379,157,404,69,21,380,165,412,73,25,388,166,413,74,26,389,387,167,411,72,24,408,164,76,28,384,29,409,162,77,385,410,163,75,27,386,662,665,667,663,189,346,520,10,37,347,38,190,521,11,36,345,191,519,9,342,40,188,516,6,41,343,186,517,7,39,344,187,518,8,35,352,180,526,0,33,353,181,527,2,1,34,351,182,525,348,31,183,522,4,523,349,32,184,5,350,30,185,524,3,695,693,696,690,370,586,604,358,258,587,259,371,605,359,260,585,369,603,357,582,261,366,600,354,262,583,367,601,355,263,584,368,602,356,264,592,376,610,364,265,593,377,611,365,363,266,591,375,609,588,267,372,606,360,607,589,268,373,361,590,269,374,608,362,673,688,675,685,598,204,14,400,194,205,192,599,12,401,193,206,597,13,399,207,197,594,17,396,195,208,595,15,397,196,209,596,16,398,200,647,651,644,648,198,655,659,653,656,640,199,639,643,636,618,203,619,612,614,621,623,201,627,624,631,202,635,629,632,699,700,702,698,496,130,224,574,103,131,104,497,222,575,102,129,495,223,573,126,106,492,227,570,107,127,493,225,571,105,128,494,226,572,101,121,502,230,580,99,122,503,228,581,579,100,120,501,229,124,97,498,233,576,231,125,98,499,577,123,96,500,232,578,670,672,668,669,508,58,51,168,304,59,305,509,52,169,303,57,507,53,170,54,300,504,50,171,301,55,505,48,172,302,56,506,49,173,295,64,514,42,174,296,65,515,43,175,176,294,63,513,44,60,298,510,45,177,46,61,299,511,178,62,297,512,47,179,683,687,681,677 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#87aba77d55a93960597d69a42bda986d959be94fa8d2c920629e2ba026b38a72, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 45.

last edited by qawbecrdtey at 2026-10-03 19:08:04 · history