Equation 677 Database

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Magma a9491fb1393c…

magma a9491fb1393c
Size
381
Isomorphism class hash
a9491fb1393cebc25ad0d301340aa5f4f88700f431265866371f1e75fdf0a091
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:40:13
Display reorder
380,314,162,143,159,156,183,141,169,148,171,163,315,184,157,142,167,144,160,146,172,313,161,145,158,155,182,140,168,147,170,128,311,153,149,135,175,177,125,179,137,129,312,154,150,136,173,178,126,180,138,130,310,152,151,134,174,176,127,181,139,133,131,166,164,165,132,375,358,344,346,376,378,334,377,333,345,327,57,10,54,51,47,5,64,12,35,58,328,48,52,6,62,8,55,13,36,326,56,9,53,50,49,7,63,11,37,23,324,17,16,30,39,41,20,46,32,24,325,18,14,31,40,42,21,44,33,25,323,19,15,29,38,43,22,45,34,28,26,61,59,60,27,332,373,366,372,338,337,353,339,365,354,304,297,250,294,291,290,248,273,252,278,298,305,288,292,246,274,251,295,253,276,306,299,249,296,293,289,247,275,254,277,266,307,260,256,242,279,284,263,286,244,264,308,258,257,240,280,282,261,287,245,265,309,259,255,241,281,283,262,285,243,268,269,270,271,272,267,351,349,359,370,361,348,350,379,371,360,317,105,86,102,99,95,84,112,91,114,106,318,96,100,85,110,87,103,89,115,316,104,88,101,98,97,83,111,90,113,71,320,65,92,78,118,120,68,122,80,72,321,66,93,79,116,121,69,123,81,73,319,67,94,77,117,119,70,124,82,76,74,109,107,108,75,342,340,341,368,357,374,355,343,367,356,301,218,202,215,212,211,230,225,3,227,219,300,209,213,231,226,200,216,4,228,329,220,201,217,214,210,232,224,2,229,190,303,238,0,194,234,205,187,207,199,188,302,239,1,195,235,203,185,208,197,189,322,237,236,196,233,204,186,206,198,192,193,222,223,221,191,363,331,369,335,362,364,330,347,336,352 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#b1211ae78f1953cbb4b5dc9dd74f3adf692aab68f9babb6f9e69bfbb6cb7816f, M = {66} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:40:14 · history