Equation 677 Database

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Magma 0662f50095d9…

magma 0662f50095d9
Size
705
Isomorphism class hash
0662f50095d908124fa6e48e7ce6fedea11690696fdf0f1e8d85166f4cb35fe0
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 19:19:01
Display reorder
660,550,345,332,71,35,69,551,346,330,33,347,70,549,331,34,67,546,344,335,31,68,547,342,333,32,66,548,343,334,30,556,336,327,77,41,557,337,328,75,39,555,338,329,76,40,552,339,326,73,37,553,340,324,74,38,554,341,325,72,36,674,677,683,686,270,44,286,11,126,9,271,42,287,127,43,10,272,285,128,7,273,47,282,129,8,274,45,283,130,6,275,46,284,131,268,50,277,2,124,269,48,278,1,125,267,49,276,0,123,264,53,280,5,120,265,51,281,3,121,266,52,279,4,122,669,672,661,663,65,352,562,134,514,132,63,353,563,515,351,133,64,561,513,137,61,348,558,510,135,62,349,559,511,136,60,350,560,512,56,358,568,140,520,54,359,569,138,521,55,357,567,139,519,59,354,564,143,516,57,355,565,141,517,58,356,566,142,518,673,681,687,684,364,15,93,240,608,241,365,16,94,606,17,242,363,95,607,243,360,14,92,611,244,361,12,90,609,245,362,13,91,610,646,645,644,246,651,654,653,652,247,659,638,636,637,248,643,614,612,613,249,616,622,621,620,250,627,630,629,628,251,635,701,704,698,697,526,303,574,183,430,184,527,304,575,431,305,185,525,573,429,182,522,302,570,426,180,523,300,571,427,181,524,301,572,428,532,309,580,189,436,533,310,581,190,437,531,311,579,191,435,528,308,576,188,432,529,306,577,186,433,530,307,578,187,434,695,692,694,696,26,154,502,230,388,228,24,155,503,389,153,229,25,501,387,233,29,150,498,384,231,27,151,499,385,232,28,152,500,386,21,145,508,236,394,22,146,509,234,395,23,144,507,235,393,20,148,504,239,390,18,149,505,237,391,19,147,506,238,392,667,662,670,666,96,490,418,78,210,79,97,491,419,211,489,80,98,417,212,81,99,486,414,213,82,100,487,415,214,83,101,488,416,215,102,496,424,84,208,103,497,425,85,209,104,495,423,86,207,105,492,420,87,204,106,493,421,88,205,107,494,422,89,206,693,689,690,691,478,376,460,222,406,223,479,377,461,407,375,224,477,459,405,225,474,372,456,402,226,475,373,457,403,227,476,374,458,404,484,382,466,220,412,485,383,467,221,413,483,381,465,219,411,480,378,462,216,408,481,379,463,217,409,482,380,464,218,410,675,676,680,679,454,472,369,118,400,119,455,473,370,401,471,117,453,371,399,114,450,468,368,396,115,451,469,366,397,116,452,470,367,398,649,650,647,109,648,657,658,655,110,656,641,642,639,108,640,618,619,617,112,615,625,626,623,113,624,633,634,631,111,632,703,700,702,699,260,442,538,292,586,293,258,443,539,587,441,291,259,537,585,288,263,438,534,582,289,261,439,535,583,290,262,440,536,584,255,448,544,298,592,256,449,545,299,593,257,447,543,297,591,254,444,540,294,588,252,445,541,295,589,253,446,542,296,590,664,671,665,668,173,196,598,317,157,315,171,197,599,158,195,316,172,597,156,313,169,192,594,160,314,170,193,595,161,312,168,194,596,159,179,202,604,323,163,177,203,605,321,164,178,201,603,322,162,175,198,600,319,166,176,199,601,320,167,174,200,602,318,165,685,678,682,688 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#9c565a9fd79b154e390f38dd387d90fedf9817e0675733b83815c4693870456f, 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 19:19:02 · history