Equation 677 Database

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Magma 90d9d3db08c2…

magma 90d9d3db08c2
Size
705
Isomorphism class hash
90d9d3db08c2ed1a240518ccd4d2c47af9e48c344c4899e1b7bbfc80227e9e62
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 21:56:00
Display reorder
660,518,376,409,336,531,337,377,519,410,532,517,375,408,335,530,372,521,412,339,534,373,522,413,340,535,374,520,411,338,533,516,407,367,334,529,514,405,368,332,527,515,406,366,333,528,403,512,370,330,525,404,513,371,331,526,402,511,369,329,524,675,684,683,677,33,41,187,346,164,344,36,34,188,165,35,39,189,345,163,46,32,186,342,167,42,30,184,343,168,44,31,185,341,166,24,193,45,352,162,25,194,47,350,160,26,195,43,351,161,192,27,37,348,158,190,28,38,349,159,191,29,40,347,157,668,664,672,670,555,100,433,458,353,459,101,556,434,354,554,102,432,457,355,99,558,436,461,356,97,559,437,462,357,98,557,435,460,358,553,431,106,456,359,551,429,107,454,360,552,430,108,455,361,427,549,105,452,362,428,550,103,453,363,426,548,104,451,364,679,676,687,678,622,22,623,621,620,628,23,630,631,629,614,21,615,613,612,18,646,647,645,644,19,654,655,653,652,20,638,639,637,636,606,607,13,604,605,590,591,14,588,589,598,599,12,596,597,573,572,16,576,577,580,583,17,581,582,60,183,15,169,170,703,702,698,704,272,225,397,385,284,386,223,273,398,285,274,224,396,384,286,221,271,400,388,283,222,269,401,389,281,220,270,399,387,282,278,395,231,383,290,279,393,229,381,291,280,394,230,382,292,391,277,227,379,289,392,275,228,380,287,390,276,226,378,288,690,694,693,691,506,172,543,421,252,422,173,507,544,250,505,171,542,420,251,175,509,546,424,255,176,510,547,425,253,174,508,545,423,254,504,541,178,419,247,502,539,179,417,248,503,540,177,418,249,537,500,181,415,246,538,501,182,416,244,536,499,180,414,245,663,662,666,671,199,95,313,482,120,483,96,200,311,118,201,94,312,481,119,91,198,316,485,116,92,196,314,486,117,93,197,315,484,115,205,308,86,480,111,206,309,87,478,109,207,310,85,479,110,307,204,89,476,114,305,202,90,477,112,306,203,88,475,113,692,695,696,689,470,2,324,211,567,212,1,471,325,568,469,0,323,213,566,5,473,327,210,570,3,474,328,208,571,4,472,326,209,569,468,322,8,217,565,466,320,6,218,563,467,321,7,219,564,318,464,11,216,561,319,465,9,214,562,317,463,10,215,560,674,688,686,673,624,261,625,627,626,635,259,632,633,634,616,260,617,619,618,257,648,649,651,650,258,656,657,659,658,256,640,641,643,642,608,609,267,611,610,592,593,265,595,594,600,601,266,603,602,579,578,263,575,574,585,584,264,587,586,365,268,262,523,438,700,699,701,697,446,48,156,135,129,133,49,447,154,127,445,50,155,134,128,51,449,152,138,132,52,450,153,136,130,53,448,151,137,131,444,147,54,141,124,442,145,55,139,125,443,146,56,140,126,150,440,57,144,123,148,441,58,142,121,149,439,59,143,122,669,661,665,667,62,235,297,494,78,495,236,63,298,76,61,237,296,493,77,234,65,293,497,74,232,66,294,498,75,233,64,295,496,73,68,303,241,492,84,69,304,242,490,82,67,302,243,491,83,299,71,240,488,80,300,72,238,489,81,301,70,239,487,79,681,682,685,680 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#fd865ad85ec1badfd7a7711949755519f1db0e961ea1bdb330ad04fd991385b2, 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 21:56:01 · history