Equation 677 Database

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Magma b7b990b2c2ad…

magma b7b990b2c2ad
Size
705
Isomorphism class hash
b7b990b2c2ad31bf779401580910fbe1923a7748b8fd3468c7474e40016b17f1
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 21:11:49
Display reorder
660,154,22,575,439,499,155,23,576,440,500,153,577,441,501,24,150,574,25,438,498,151,572,26,436,496,152,573,27,437,497,145,581,28,445,505,446,146,582,29,506,144,583,30,447,507,580,148,31,444,504,578,149,32,442,502,579,147,33,443,503,678,677,685,684,278,427,369,393,403,279,428,367,391,404,280,368,392,405,429,281,365,426,389,402,282,366,424,390,400,283,364,425,388,401,276,375,433,399,409,397,277,373,434,410,275,374,435,398,411,371,272,432,395,408,372,273,430,396,406,370,274,431,394,407,663,667,664,661,335,291,415,379,519,336,292,416,380,520,334,417,381,521,290,338,414,294,378,518,339,412,295,376,516,337,413,293,377,517,333,421,289,385,525,386,331,422,287,526,332,423,288,387,527,420,329,285,384,524,418,330,286,382,522,419,328,284,383,523,679,675,674,676,38,143,511,313,218,39,141,512,311,219,37,513,312,220,142,34,510,139,309,221,35,508,140,310,222,36,509,138,308,223,44,641,637,640,639,648,45,649,645,647,43,657,653,656,655,630,40,629,633,632,514,41,0,315,216,515,42,1,314,217,703,698,704,697,162,487,587,451,240,163,488,588,452,241,164,589,453,239,489,165,586,486,450,236,166,584,484,448,237,167,585,485,449,238,160,593,493,457,246,458,161,594,494,247,159,595,495,459,245,592,156,492,456,242,590,157,490,454,243,591,158,491,455,244,693,690,691,694,297,215,463,343,198,298,213,464,344,199,296,465,345,200,214,300,462,211,342,201,301,460,212,340,202,299,461,210,341,203,303,469,206,349,196,350,304,470,204,197,302,471,205,351,195,468,306,209,348,192,466,307,207,346,193,467,305,208,347,194,670,662,672,666,68,72,176,111,266,69,70,174,109,267,67,175,110,268,71,64,179,75,107,269,65,177,73,108,270,66,178,74,106,271,59,171,78,117,264,115,60,172,76,265,58,173,77,116,263,170,62,81,113,260,168,63,79,114,261,169,61,80,112,262,695,689,696,692,46,190,355,619,543,47,191,356,620,544,48,357,621,545,189,49,354,186,618,542,50,352,187,616,540,51,353,188,617,541,52,361,181,625,549,626,53,362,182,550,54,363,180,627,551,360,55,184,624,548,358,56,185,622,546,359,57,183,623,547,681,688,683,673,118,611,18,555,132,119,612,19,556,130,120,20,557,131,613,121,17,610,554,135,122,15,608,552,133,123,16,609,553,134,124,636,643,642,638,650,125,644,651,646,126,652,659,658,654,634,127,635,631,628,21,128,614,558,136,14,129,615,559,137,701,699,702,700,317,475,563,224,10,318,476,564,225,8,316,565,226,9,477,320,562,474,227,13,321,560,472,228,11,319,561,473,229,12,323,569,481,230,5,231,324,570,482,6,322,571,483,232,7,568,326,480,233,4,566,327,478,234,2,567,325,479,235,3,665,669,668,671,252,104,531,84,599,253,105,532,82,600,251,533,83,601,103,248,530,100,87,598,249,528,101,85,596,250,529,102,86,597,258,537,95,90,605,88,259,538,96,606,257,539,94,89,607,536,254,98,93,604,534,255,99,91,602,535,256,97,92,603,686,687,682,680 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#dcedbe28d6e821630efaff61054e89b4af79513af364c6246d7e9f07a2213221, 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 21:11:50 · history