Equation 677 Database

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Magma d156417c1abe…

magma d156417c1abe
Size
705
Isomorphism class hash
d156417c1abe88c2ffea92ee2513ad10fedbd8f343db103ccda909b88b2e936e
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 20:46:06
Display reorder
660,355,270,418,421,549,271,419,422,356,550,417,269,420,354,548,266,414,424,358,552,267,415,425,359,553,268,416,423,357,551,261,409,427,361,555,262,410,428,362,556,260,408,426,360,554,412,264,430,364,558,413,265,431,365,559,411,263,429,363,557,675,683,673,677,129,201,231,120,73,202,232,121,130,71,230,200,119,128,72,204,234,116,132,69,205,235,117,133,70,203,233,118,131,68,207,229,126,135,79,208,227,127,136,77,206,228,125,134,78,225,210,122,138,75,226,211,123,139,76,224,209,124,137,74,669,662,672,661,90,115,244,251,525,113,242,252,91,526,243,114,253,89,524,111,247,250,86,528,112,245,248,87,529,110,246,249,88,527,106,239,257,81,531,104,240,258,82,532,105,241,259,80,530,238,109,256,84,534,236,107,254,85,535,237,108,255,83,533,679,681,684,674,30,101,469,399,39,102,470,400,28,37,468,103,398,29,38,100,472,402,33,35,98,473,403,31,36,99,471,401,32,34,92,475,405,25,43,93,476,406,26,41,94,474,404,27,42,647,95,646,648,649,658,96,657,652,653,477,97,407,24,40,703,698,704,700,165,278,162,597,537,279,163,598,166,538,161,280,596,164,536,281,158,600,168,540,282,159,601,169,541,283,160,599,167,539,276,153,603,171,543,277,154,604,172,544,275,152,602,170,542,156,272,606,174,546,157,273,607,175,547,155,274,605,173,545,693,692,689,694,561,21,349,457,513,22,350,458,562,514,348,23,456,560,512,20,352,460,564,516,18,353,461,565,517,19,351,459,563,515,12,347,463,567,519,13,345,464,568,520,14,346,462,566,518,343,15,466,570,522,344,16,467,571,523,342,17,465,569,521,668,666,667,664,58,185,292,299,327,186,290,300,56,328,291,187,301,57,326,184,295,298,61,330,182,293,296,59,331,183,294,297,60,329,176,287,305,64,325,177,288,306,62,323,178,289,307,63,324,286,179,304,67,321,284,180,302,65,322,285,181,303,66,320,695,691,696,690,433,318,573,6,633,319,574,7,434,634,572,317,8,432,632,314,576,9,436,636,315,577,10,437,637,316,575,11,435,635,309,579,4,439,639,310,580,5,440,640,308,578,3,438,638,582,312,1,442,642,583,313,0,443,643,581,311,2,441,641,678,688,685,682,374,192,479,337,378,193,480,335,375,376,478,191,336,373,377,188,482,333,370,381,189,483,334,371,379,190,481,332,372,380,198,485,341,368,384,199,486,339,369,382,197,484,340,367,383,651,194,650,645,644,659,195,654,656,655,487,196,338,366,385,699,702,701,697,501,144,445,213,621,145,446,214,502,622,444,143,212,500,620,140,448,216,504,624,141,449,217,505,625,142,447,215,503,623,150,451,219,507,627,151,452,220,508,628,149,450,218,506,626,454,146,222,510,630,455,147,223,511,631,453,148,221,509,629,665,671,663,670,489,50,387,609,585,51,388,610,490,586,386,52,608,488,584,53,390,612,492,588,54,391,613,493,589,55,389,611,491,587,48,393,615,495,591,49,394,616,496,592,47,392,614,494,590,396,44,618,498,594,397,45,619,499,595,395,46,617,497,593,680,686,676,687 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#d368fcffc98defb742f81d5388b25ae4c38c7de7079297526f4ed93fca5d0bec, 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 20:46:07 · history