Equation 677 Database

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Magma 5330ee86aeb3…

magma 5330ee86aeb3
Size
705
Isomorphism class hash
5330ee86aeb3ed0b26d4f9587a7715b43c3cba8ff5e2bb807bcc6b90a134af45
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 16:46:41
Display reorder
660,491,490,489,486,487,488,481,482,480,484,485,483,476,306,307,474,308,475,309,479,310,477,311,478,304,471,305,472,303,473,300,470,301,468,302,469,463,503,464,501,462,502,466,499,467,500,465,498,461,494,459,492,460,493,457,497,458,495,456,496,677,683,679,691,165,167,166,163,164,162,158,156,157,161,159,160,198,643,644,199,642,200,646,201,647,202,645,203,641,196,639,197,640,195,637,192,638,193,636,194,180,176,181,174,182,175,183,179,184,177,185,178,186,171,187,172,188,173,189,170,190,168,191,169,662,668,665,671,346,345,347,344,342,343,336,337,338,339,340,341,332,31,32,330,30,331,34,335,35,333,33,334,29,327,27,328,28,329,25,326,26,324,24,325,312,352,313,353,314,351,315,348,316,349,317,350,318,358,319,359,320,357,321,354,322,355,323,356,678,684,673,688,220,219,221,218,216,217,225,226,227,224,222,223,204,128,126,205,127,206,131,207,129,208,130,209,123,210,124,211,125,212,122,213,120,214,121,215,242,230,240,228,241,229,245,233,243,231,244,232,248,236,246,234,247,235,251,239,249,237,250,238,697,702,699,704,547,546,548,549,550,551,544,545,543,540,541,542,538,54,55,539,56,537,57,534,58,535,59,536,52,529,53,530,51,528,48,532,49,533,50,531,519,505,520,506,521,504,518,508,516,509,517,507,525,511,526,512,527,510,524,514,522,515,523,513,687,694,692,698,288,290,289,293,291,292,296,294,295,299,297,298,279,46,47,280,45,281,42,278,43,276,44,277,37,285,38,286,36,287,40,284,41,282,39,283,115,413,116,411,114,412,118,409,119,410,117,408,113,419,111,417,112,418,109,415,110,416,108,414,663,667,666,672,566,565,564,568,569,567,571,572,570,574,575,573,555,256,257,556,255,557,252,554,253,552,254,553,262,561,263,562,261,563,258,560,259,558,260,559,133,587,134,585,132,586,136,583,137,584,135,582,139,578,140,576,138,577,142,581,143,579,141,580,686,693,689,695,364,363,365,362,360,361,369,370,371,368,366,367,397,275,273,398,274,396,271,400,272,401,270,399,266,403,264,404,265,402,269,406,267,407,268,405,392,372,390,373,391,374,395,375,393,376,394,377,387,378,388,379,389,380,386,381,384,382,385,383,675,682,680,690,622,621,623,620,618,619,612,613,614,615,616,617,607,144,145,608,146,606,147,610,148,611,149,609,150,605,151,603,152,604,153,601,154,602,155,600,597,628,598,629,599,627,596,624,594,625,595,626,588,634,589,635,590,633,591,630,592,631,593,632,696,701,700,703,70,69,71,68,66,67,60,61,62,63,64,65,75,85,86,76,84,77,88,74,89,72,87,73,91,81,92,82,90,83,94,80,95,78,93,79,654,3,655,4,656,5,657,2,658,1,659,0,652,9,653,10,651,11,648,8,649,6,650,7,661,669,664,670,98,97,96,100,101,99,103,104,102,106,107,105,455,22,23,453,21,454,18,451,19,452,20,450,13,446,14,444,12,445,16,449,17,447,15,448,434,424,432,425,433,423,437,420,435,421,436,422,440,430,438,431,439,429,443,426,441,427,442,428,676,681,674,685 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#3e7f78778326128ca89bcdb69266df7c07c66aee73c2a2e36b24ead92b52079d, M = {62} 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 16:46:42 · history