Equation 677 Database

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Magma e055a5752adc…

magma e055a5752adc
Size
381
Isomorphism class hash
e055a5752adc55ad76b358777f210666935a061d3c760f7014c93d56b4b75c2a
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 23:38:26
Display reorder
380,20,35,21,16,17,44,15,43,32,39,128,145,129,123,124,125,110,121,122,142,178,195,179,173,174,175,160,171,172,192,228,245,229,223,224,225,210,221,222,242,319,313,314,315,316,78,95,79,73,74,75,60,71,72,92,278,295,279,274,273,275,260,271,272,292,322,358,362,346,356,376,363,359,334,357,374,14,47,42,31,34,19,36,48,49,18,120,147,119,141,144,127,126,146,148,149,170,197,169,191,194,177,176,196,198,199,220,247,219,241,244,227,226,246,248,249,301,300,311,309,312,70,97,69,91,94,77,76,96,98,99,270,297,269,291,294,277,276,296,298,299,328,373,355,361,379,331,354,377,360,378,330,27,26,25,11,41,30,37,4,46,33,136,137,134,115,116,140,143,104,105,135,187,186,184,165,166,190,193,154,155,185,237,236,234,215,216,240,243,204,205,235,308,318,310,317,307,86,87,84,65,66,90,93,54,55,85,287,286,284,265,266,290,293,254,255,285,320,333,368,372,339,332,369,351,375,340,343,24,12,45,40,10,29,5,38,13,28,132,117,133,114,113,139,138,106,107,118,182,167,183,164,163,189,188,156,157,168,232,217,233,214,213,239,238,206,207,218,303,306,304,305,302,82,67,83,64,63,89,88,56,57,68,282,267,283,264,263,289,288,256,257,268,321,350,366,371,341,352,367,349,370,342,353,3,9,2,0,1,22,6,7,8,23,103,112,102,100,101,130,131,108,109,111,153,162,152,150,151,180,181,158,159,161,203,212,202,200,201,230,231,208,209,211,326,327,329,323,324,53,62,52,50,51,80,81,58,59,61,253,262,252,250,251,280,281,258,259,261,325,336,338,364,344,348,337,335,365,345,347 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#a5dba37ae82f5d1e2c854105d6ba510f1387eb5ee3dcc59dd48a683e84cf35f4, M = {76} 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 23:38:27 · history