Equation 677 Database

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Magma 5d9cdd9364bb…

magma 5d9cdd9364bb
Size
705
Isomorphism class hash
5d9cdd9364bb02f06e38b4006d886d98879aba41842794bcb4e20beb0e1faf71
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 20:34:52
Display reorder
660,534,62,33,18,491,34,532,19,489,60,35,61,533,20,490,65,32,530,21,487,63,30,531,22,488,64,31,529,23,486,540,24,68,16,497,538,25,66,17,495,539,26,67,15,496,27,536,71,12,493,28,537,69,13,494,14,29,535,70,492,687,678,681,679,286,159,275,319,301,273,287,320,302,157,274,158,285,318,300,162,278,289,315,297,160,276,290,316,298,161,277,288,317,299,292,281,154,310,307,293,279,155,311,308,291,280,156,309,306,284,295,153,313,303,282,296,151,314,304,312,283,294,152,305,666,672,670,661,39,325,577,510,422,575,40,508,420,326,576,324,41,509,421,321,573,38,506,418,322,574,36,507,419,323,572,37,505,417,45,583,331,516,428,46,581,332,514,426,47,582,330,515,427,579,44,327,512,424,580,42,328,513,425,511,578,43,329,423,680,675,673,685,503,172,187,180,458,188,501,178,456,173,186,174,502,179,457,171,183,499,176,454,169,184,500,177,455,170,185,498,175,453,658,652,163,654,655,642,636,164,638,639,650,644,165,646,647,621,623,166,624,625,630,634,167,628,631,181,144,504,168,459,703,697,701,704,222,7,212,589,230,210,223,587,228,8,211,6,224,588,229,10,208,221,585,226,11,209,219,586,227,9,207,220,584,225,213,203,5,595,236,214,201,3,593,234,215,202,4,594,235,206,216,0,591,232,204,217,2,592,233,590,205,218,1,231,693,692,689,691,92,142,410,446,438,408,90,444,439,143,409,141,91,445,440,138,406,95,442,437,139,407,93,443,435,140,405,94,441,436,87,416,133,452,429,88,414,134,450,430,89,415,132,451,431,412,86,136,448,432,413,84,137,449,433,447,411,85,135,434,664,663,669,662,354,258,386,379,361,384,355,380,362,259,385,260,356,378,360,257,382,353,375,357,255,383,351,376,358,256,381,352,377,359,345,392,249,370,367,346,390,250,371,368,347,391,251,369,366,388,348,252,373,363,389,349,253,374,364,372,387,350,254,365,694,695,696,690,338,59,393,472,613,394,336,470,611,57,395,58,337,471,612,55,396,334,468,609,56,397,335,469,610,54,398,333,467,608,344,399,50,478,619,342,400,48,476,617,343,401,49,477,618,402,340,53,474,615,403,341,51,475,616,473,404,339,52,614,677,688,674,676,464,266,567,484,150,565,465,482,148,264,566,265,466,483,149,262,570,463,480,146,263,568,461,481,147,261,569,462,479,145,656,659,272,657,653,640,643,270,641,637,648,651,271,649,645,627,626,268,622,620,635,632,269,633,629,485,571,460,267,182,700,698,699,702,196,76,601,551,552,599,197,548,547,77,600,75,195,550,549,72,597,199,543,544,73,598,200,545,546,74,596,198,542,541,194,607,82,563,564,192,605,83,560,559,193,606,81,561,562,603,190,78,555,556,604,191,79,557,558,554,602,189,80,553,668,667,665,671,244,102,522,124,117,520,245,125,118,103,521,104,243,123,119,105,518,247,120,116,106,519,248,121,114,107,517,246,122,115,242,528,100,130,108,240,526,101,131,109,241,527,99,129,110,524,238,96,126,111,525,239,97,127,112,128,523,237,98,113,686,682,684,683 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#c633edfa20dc6722982152bc303db7386181f99f3fbdfeb33272ccd5420b69f5, 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 20:34:53 · history