Equation 677 Database

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Magma 54e64887f961…

magma 54e64887f961
Size
595
Isomorphism class hash
54e64887f961f11bdf7a2c9cd23d518fb678e0d17780843ab585cd38f226c974
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
2026-10-08 08:36:26
Display reorder
69,68,70,71,66,67,57,56,58,53,54,55,140,139,141,136,137,138,485,484,483,482,481,480,476,474,475,479,477,478,520,519,551,576,555,264,261,169,262,263,211,177,19,15,16,17,18,114,113,115,116,117,112,12,14,11,220,221,13,239,238,188,187,79,80,37,36,38,39,40,229,208,255,205,254,206,207,226,183,227,184,228,182,176,0,1,2,3,4,355,354,356,358,359,357,452,451,450,453,454,455,445,444,446,447,448,449,459,461,460,458,456,457,499,498,500,503,501,502,413,412,411,408,409,410,312,314,313,315,316,317,531,546,517,538,539,518,511,553,548,559,569,585,562,588,547,575,6,8,7,10,5,9,75,74,76,77,72,73,49,48,50,51,52,47,132,131,133,134,135,130,127,126,128,129,124,125,95,99,96,97,98,241,223,23,224,225,181,180,232,231,65,233,230,185,189,83,84,85,81,82,299,298,297,296,294,295,505,504,506,507,508,509,390,392,391,395,393,394,387,389,388,386,384,385,331,330,332,335,333,334,427,426,428,431,429,430,425,424,423,422,420,421,540,541,535,516,532,533,545,557,573,572,550,571,574,560,561,554,105,101,100,103,104,102,62,61,63,64,59,60,46,45,41,42,43,44,29,28,24,25,26,27,150,149,151,152,147,148,143,146,144,145,142,280,286,175,287,283,278,279,282,284,173,285,281,274,248,162,158,159,160,161,327,329,328,324,325,326,472,471,473,470,469,468,291,293,292,290,289,288,400,399,401,396,397,398,360,362,361,364,365,363,466,464,467,463,465,462,418,417,419,415,416,414,525,527,510,515,514,513,512,552,563,578,556,594,577,567,582,592,92,94,93,90,91,89,172,273,216,271,217,272,215,214,265,212,266,213,240,190,191,86,87,88,166,165,167,168,260,259,164,256,257,209,210,258,199,249,200,250,201,202,246,198,247,196,245,197,186,237,234,78,235,236,302,301,300,305,303,304,336,338,337,340,341,339,382,381,383,378,379,380,406,405,407,402,403,404,493,492,494,497,495,496,373,372,374,377,375,376,323,322,321,320,318,319,542,543,521,526,523,522,537,591,564,587,589,583,586,565,558,581,34,30,35,32,33,31,170,268,269,171,270,267,219,218,275,276,174,277,222,179,178,20,21,22,156,155,157,154,195,244,243,242,194,192,193,153,122,121,123,118,119,120,109,108,110,111,106,107,163,204,252,253,251,203,442,441,443,439,440,438,488,486,487,489,490,491,368,367,366,370,371,369,434,433,432,436,437,435,306,308,307,310,311,309,348,350,349,352,353,351,347,346,345,344,342,343,536,534,524,529,530,528,544,590,549,580,593,570,579,566,584,568 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#be842e4d65ca083f5f61a36963819b0aa7d50180968070250538ce7f22ff68d2, M = the submagma generated by {6, 24} (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 2026-10-08 08:36:27 · history