Equation 677 Database

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Magma c9e7d62d1870…

magma c9e7d62d1870
Size
399
Isomorphism class hash
c9e7d62d1870923b7f53beab88e2dc47e495a0f8908fc06c48df5712f7b4f1cb
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-08 04:39:40
Display reorder
214,215,207,208,209,210,211,212,213,198,199,200,201,202,203,204,205,206,381,170,87,1,192,193,162,88,0,194,163,89,2,195,164,81,3,82,196,165,4,197,166,83,5,189,167,84,6,190,168,85,7,169,191,86,8,185,80,179,9,186,72,171,10,187,73,172,11,188,74,173,12,180,75,174,13,181,76,175,14,182,77,176,15,183,78,177,16,184,79,178,17,392,386,385,391,235,64,333,298,299,236,65,334,300,237,66,335,301,238,67,336,68,302,239,337,303,240,69,338,304,241,70,339,305,242,71,340,234,297,63,341,291,57,244,326,292,58,245,327,293,59,246,328,294,60,247,329,295,61,248,330,296,62,249,331,288,54,250,332,289,55,251,324,290,56,243,325,384,390,389,383,263,306,216,45,46,264,307,217,47,265,308,218,48,266,309,219,310,49,267,220,50,268,311,221,51,269,312,222,52,261,313,223,262,53,314,224,38,315,256,225,39,316,257,226,40,317,258,227,41,318,259,228,42,319,260,229,43,320,252,230,44,321,253,231,36,322,254,232,37,323,255,233,387,398,397,388,273,349,342,34,35,274,351,344,27,275,353,346,28,276,355,348,357,29,277,350,30,278,359,352,31,270,343,354,32,271,345,356,272,33,347,358,18,367,282,360,19,369,283,362,20,371,284,364,21,373,285,366,22,375,286,368,23,376,287,370,24,361,279,372,25,363,280,374,26,365,281,377,393,395,396,394,110,141,106,156,157,111,142,107,158,112,143,99,159,113,135,100,136,160,114,101,161,115,137,102,153,116,138,103,154,108,139,104,109,155,140,105,149,134,119,90,150,126,120,91,151,127,121,92,152,128,122,93,144,129,123,94,145,130,124,95,146,131,125,96,147,132,117,97,148,133,118,98,380,382,378,379 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#c59c8e5ced2598ef60b088e5e1fcfd60cc5d57630eecc4c2b2566eabfd451eb5, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-08 04:39:41 · history