Equation 677 Database

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Magma c87aa2684dc4…

magma c87aa2684dc4
Size
595
Isomorphism class hash
c87aa2684dc44fba889ecc3a70ba39a756bda507f80a3bc259cf18849b6a1612
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 09:37:39
Display reorder
16,15,17,12,13,14,28,27,29,24,25,26,389,388,387,386,384,385,302,301,300,304,305,303,474,475,476,477,478,479,530,533,520,566,552,258,257,161,255,256,200,199,156,157,158,159,160,21,20,22,23,18,19,87,86,88,237,236,85,214,215,170,171,0,1,165,164,166,167,168,266,208,267,209,268,206,207,224,180,225,181,226,182,188,115,116,112,113,114,283,284,282,285,286,287,495,497,496,494,493,492,464,463,462,466,467,465,438,440,439,443,441,442,501,503,502,499,500,498,371,370,369,366,367,368,399,401,400,396,397,398,540,546,534,536,527,535,532,569,549,548,592,587,556,551,570,588,30,35,31,32,33,34,90,91,92,93,94,89,110,109,111,106,107,108,142,141,143,144,145,146,124,123,119,120,121,122,99,98,95,96,97,238,241,117,239,240,189,190,230,229,69,227,228,183,185,80,81,77,78,79,316,315,317,313,314,312,327,329,328,326,324,325,469,470,468,473,471,472,321,323,322,320,318,319,460,459,461,458,456,457,299,298,297,294,295,296,504,509,506,508,505,507,539,528,514,522,512,513,547,583,575,572,564,563,558,568,562,561,147,152,148,149,150,151,73,74,75,70,71,72,59,58,60,61,62,57,7,6,8,9,10,5,41,40,42,43,44,45,134,132,135,131,133,274,280,169,281,277,272,273,275,278,163,279,276,265,223,46,47,48,49,50,289,288,290,292,293,291,437,436,435,433,434,432,422,421,420,424,425,423,445,444,446,447,448,449,347,346,345,342,343,344,408,410,409,412,413,411,363,365,364,360,361,362,538,542,515,511,523,521,518,577,554,594,578,559,591,571,580,584,130,129,125,126,127,128,153,248,197,249,198,250,179,178,219,176,220,177,216,173,172,2,3,4,37,36,38,39,221,222,11,218,217,175,174,269,211,271,213,270,210,212,259,202,260,203,261,201,184,234,231,76,232,233,353,352,351,350,348,349,451,450,452,453,454,455,485,484,483,480,482,481,377,376,375,373,374,372,418,417,419,416,414,415,381,383,382,379,380,378,356,355,354,359,357,358,541,545,531,529,525,524,526,550,553,593,557,585,589,555,560,576,65,64,66,67,68,63,155,253,254,154,251,252,191,192,242,243,118,244,235,186,187,83,84,82,137,136,138,139,193,245,247,246,194,195,196,140,102,101,103,104,105,100,54,53,55,56,51,52,162,205,262,263,264,204,341,340,339,338,336,337,405,407,406,404,402,403,308,307,306,310,311,309,330,332,331,335,333,334,487,488,486,490,491,489,429,431,430,427,428,426,393,395,394,390,391,392,537,543,517,519,510,516,544,579,581,567,582,586,573,574,590,565 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#3577482bd341efd08404d9d1bdf0973fd33301f1401bf0112f6bd2c4e9ff916f, M = the submagma generated by {48, 60} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-06 09:37:40 · history