Equation 677 Database

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Magma 6012d08ddd3a…

magma 6012d08ddd3a
Size
705
Isomorphism class hash
6012d08ddd3aae10e46e9ef5ff1e366bcdc40da896fff6299abeaabed9b5032c
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 15:57:05
Display reorder
660,242,419,42,224,555,243,420,225,43,556,241,421,41,223,557,418,238,38,220,554,416,239,39,221,552,417,240,40,222,553,425,230,233,33,561,426,231,234,34,562,427,229,232,32,563,226,424,236,36,560,227,422,237,37,558,228,423,235,35,559,676,683,680,684,9,143,402,487,50,10,144,488,403,51,8,142,401,489,52,146,12,398,486,53,147,13,399,484,54,145,11,400,485,55,141,493,15,393,48,139,494,16,394,49,140,495,14,392,47,492,137,18,396,44,490,138,19,397,45,491,136,17,395,46,664,672,661,667,132,499,25,339,475,130,500,340,23,476,131,501,24,341,477,498,135,21,338,474,496,133,22,336,472,497,134,20,337,473,505,345,127,31,481,506,346,128,29,482,507,347,129,30,483,344,504,126,27,480,342,502,124,28,478,343,503,125,26,479,678,677,687,673,431,332,81,4,622,432,330,2,82,620,433,331,80,3,621,335,430,84,7,625,333,428,85,5,623,334,429,83,6,624,638,637,640,87,643,646,645,648,88,651,654,653,656,86,659,629,630,631,90,632,0,328,434,91,626,1,329,435,89,627,704,702,697,699,269,251,75,567,282,270,252,568,76,280,268,250,74,569,281,254,272,78,566,285,255,273,79,564,283,253,271,77,565,284,249,573,275,73,288,247,574,276,71,286,248,575,274,72,287,572,245,278,69,291,570,246,279,70,289,571,244,277,68,290,690,689,694,695,194,217,327,463,205,195,218,464,325,206,193,219,326,465,207,216,190,323,462,204,214,191,324,460,202,215,192,322,461,203,208,469,185,318,196,209,470,186,316,197,210,471,184,317,198,468,211,188,321,199,466,212,189,319,200,467,213,187,320,201,668,663,670,665,266,451,167,292,439,267,452,293,168,440,265,453,166,294,441,450,262,170,295,438,448,263,171,296,436,449,264,169,297,437,457,298,257,165,445,458,299,258,163,446,459,300,256,164,447,301,456,260,161,444,302,454,261,162,442,303,455,259,160,443,692,691,696,693,375,356,176,362,311,376,354,360,177,312,377,355,175,361,310,359,374,172,365,314,357,372,173,363,315,358,373,174,364,313,351,368,381,182,309,352,366,382,183,307,353,367,383,181,308,371,350,380,178,305,369,348,378,179,306,370,349,379,180,304,682,685,675,674,387,523,106,578,119,388,524,576,104,120,389,525,105,577,121,522,386,109,581,118,520,384,107,579,116,521,385,108,580,117,641,642,639,112,636,649,650,647,110,644,657,658,655,111,652,635,634,633,115,628,582,526,390,113,122,583,527,391,114,123,700,701,703,698,93,407,59,543,599,94,408,544,60,600,92,409,61,545,601,406,96,58,542,598,404,97,56,540,596,405,95,57,541,597,413,549,99,65,605,414,550,100,66,606,415,551,98,67,607,548,412,102,64,604,546,410,103,62,602,547,411,101,63,603,662,671,666,669,511,587,156,611,531,512,588,612,154,532,513,589,155,613,533,586,510,159,610,530,584,508,157,608,528,585,509,158,609,529,593,617,517,151,537,594,618,518,152,538,595,619,519,153,539,616,592,516,150,536,614,590,514,148,534,615,591,515,149,535,686,681,679,688 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#25532901b7174194dca0f8f453aa2ae473cc5b2aa34d04b35f0c3beb206af29c, 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 15:57:11 · history