Equation 677 Database

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Magma 120b1989a095…

magma 120b1989a095
Size
705
Isomorphism class hash
120b1989a09529ed4f53493ab50998804ee84afefa7156630508d742bf04ff61
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 18:09:03
Display reorder
660,163,186,104,99,550,105,187,100,548,161,185,162,106,98,549,159,103,182,95,546,101,160,183,96,547,102,158,184,97,545,177,154,90,110,541,178,152,91,111,539,176,153,89,112,540,157,180,93,109,544,155,181,94,107,542,108,156,179,92,543,678,674,685,676,468,80,310,292,408,311,81,293,406,466,82,467,312,294,407,464,309,79,291,404,307,465,77,289,405,308,463,78,290,403,86,459,298,301,399,87,457,299,302,397,88,458,300,303,398,462,85,297,304,402,460,83,295,305,400,306,461,84,296,401,665,666,664,663,61,27,526,579,432,524,28,577,430,59,26,60,525,578,431,64,522,23,575,428,523,62,24,576,429,521,63,25,574,427,18,56,570,517,423,19,57,568,515,421,17,58,569,516,422,55,21,573,520,426,53,22,571,518,424,519,54,20,572,425,687,683,679,686,654,333,652,659,653,636,331,643,637,638,332,646,644,651,645,622,620,336,627,621,629,630,334,635,628,612,614,335,619,613,328,149,553,139,144,329,147,551,140,142,330,148,552,141,143,604,327,607,608,609,150,325,554,138,145,137,151,326,555,146,703,698,704,700,360,268,202,195,444,200,266,196,442,358,267,359,201,194,443,356,205,271,198,440,203,357,269,199,441,204,355,270,197,439,263,351,193,208,435,264,349,191,206,433,265,350,192,207,434,354,262,189,211,438,352,260,190,209,436,210,353,261,188,437,690,691,692,694,538,115,591,125,372,589,113,126,370,536,114,537,590,127,371,534,587,118,128,368,588,535,116,129,369,586,533,117,130,367,121,529,131,582,363,119,527,132,580,361,120,528,133,581,362,532,124,134,585,366,530,122,135,583,364,584,531,123,136,365,668,672,662,661,239,280,456,259,229,454,278,257,227,240,279,241,455,258,228,238,452,283,255,225,453,236,281,256,226,451,237,282,254,224,275,245,250,447,235,276,246,248,445,233,277,247,249,446,234,244,274,253,450,231,242,272,251,448,232,449,243,273,252,230,695,693,696,689,13,40,603,384,480,601,38,382,478,11,39,12,602,383,479,16,599,36,380,476,600,14,37,381,477,598,15,35,379,475,31,8,375,594,471,29,9,373,592,469,30,10,374,593,470,7,34,378,597,474,5,32,376,595,472,596,6,33,377,473,682,688,680,673,657,76,658,656,655,642,74,640,639,641,75,649,650,648,647,625,626,72,624,623,634,633,73,632,631,618,617,71,616,615,67,495,287,500,3,65,493,288,498,4,66,494,286,499,2,611,70,610,606,605,496,68,284,501,1,502,497,69,285,0,702,697,701,699,50,344,314,514,567,315,345,512,565,51,343,52,313,513,566,49,317,347,510,563,318,47,348,511,564,316,48,346,509,562,342,41,505,320,558,340,42,503,321,556,341,43,504,319,557,44,338,508,323,561,45,339,506,324,559,322,46,337,507,560,670,669,671,667,396,170,492,222,420,490,171,223,418,394,172,395,491,221,419,392,488,173,218,416,489,393,174,219,417,487,391,175,220,415,168,387,213,483,411,169,385,214,481,409,167,386,212,482,410,390,164,216,486,414,388,165,217,484,412,485,389,166,215,413,675,681,677,684 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#65ec2d14586b016399098bfd783683584e63e97f4655962a7b7e32e1fef46a76, 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 18:09:04 · history