Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma f8ecc561ddb8…

magma f8ecc561ddb8
Size
381
Isomorphism class hash
f8ecc561ddb873da3a61420c5e8a68dde3ac00a72edb0ad9df1d7affea4a9db4
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 23:22:43
Display reorder
380,287,282,278,268,273,263,109,99,104,94,84,89,176,181,170,190,196,185,59,64,52,74,79,69,47,42,297,39,27,34,13,15,22,2,292,7,245,250,255,231,236,241,304,305,303,300,302,301,128,134,138,114,118,124,160,166,155,146,151,141,210,205,200,221,225,216,332,342,345,355,351,370,379,362,337,367,285,280,277,267,271,262,108,98,102,92,81,88,178,183,173,193,198,188,57,63,50,73,77,67,45,41,295,38,25,33,11,16,20,1,290,6,247,252,257,232,237,242,324,325,326,327,328,329,129,133,139,113,119,123,162,167,157,147,152,142,212,207,202,222,227,217,330,340,347,357,352,372,376,361,336,365,286,281,276,266,272,261,107,97,103,93,83,87,177,182,172,192,197,187,58,62,51,72,78,68,46,40,296,37,26,32,12,19,21,0,291,5,246,251,256,230,235,240,313,314,312,316,317,315,127,132,137,112,117,122,161,165,156,145,150,140,211,206,201,220,226,215,331,341,346,356,350,371,375,360,335,366,289,284,275,265,270,260,105,95,100,91,82,86,179,184,174,194,199,189,56,61,54,70,75,65,49,44,299,36,29,31,14,18,24,4,294,9,249,254,259,234,239,244,306,307,308,309,310,311,125,130,135,110,115,121,164,169,159,149,154,144,214,209,204,224,229,219,334,344,349,359,354,374,378,364,339,369,288,283,279,269,274,264,106,96,101,90,80,85,175,180,171,191,195,186,55,60,53,71,76,66,48,43,298,35,28,30,10,17,23,3,293,8,248,253,258,233,238,243,321,322,323,318,319,320,126,131,136,111,116,120,163,168,158,148,153,143,213,208,203,223,228,218,333,343,348,358,353,373,377,363,338,368 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#45ae9dee612792667330602ba505951dcde187c4c1909cf40fbaf15f74e8af60, M = {67} 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 23:22:44 · history