Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 0b8b19ba4140…

magma 0b8b19ba4140
Size
381
Isomorphism class hash
0b8b19ba4140390d2e8bb1148aea979665163c8fc3648051dd5b23534e1a4f03
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 23:18:05
Display reorder
380,12,267,17,32,21,27,203,193,198,188,178,183,297,167,172,162,152,157,117,122,112,287,107,102,43,48,38,7,273,6,88,93,98,78,83,283,323,321,322,320,318,319,247,238,243,263,253,258,223,228,233,208,213,218,278,68,73,63,53,58,147,142,292,137,127,132,362,343,373,357,353,367,337,332,348,377,11,265,16,30,22,26,200,191,196,185,176,181,295,166,171,160,150,155,115,120,111,286,105,100,42,47,37,5,272,4,87,92,97,77,82,282,306,307,308,309,310,311,245,237,241,261,251,256,221,226,231,205,210,216,277,67,72,62,52,57,145,140,291,135,126,131,361,342,371,356,352,365,335,330,347,375,13,268,18,33,20,28,202,192,197,187,177,182,298,168,173,163,153,158,118,123,113,288,108,103,44,49,39,9,274,8,89,94,99,79,84,284,327,328,329,324,325,326,248,235,240,262,252,257,222,227,232,207,212,217,279,69,74,64,54,59,148,143,293,138,128,133,363,344,372,358,354,368,338,333,349,379,14,269,19,34,23,29,204,194,199,189,179,184,299,169,174,164,154,159,119,124,114,289,109,104,41,45,36,0,271,1,85,91,96,76,81,280,303,304,305,301,300,302,249,239,244,264,254,259,224,229,234,209,214,219,275,65,71,60,51,56,149,144,294,139,129,134,364,341,374,359,350,369,339,334,346,378,10,266,15,31,24,25,201,190,195,186,175,180,296,165,170,161,151,156,116,121,110,285,106,101,40,46,35,3,270,2,86,90,95,75,80,281,312,313,314,315,316,317,246,236,242,260,250,255,220,225,230,206,211,215,276,66,70,61,50,55,146,141,290,136,125,130,360,340,370,355,351,366,336,331,345,376 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#0c1c8b18119133fb8debdb5d149d6db1ac93e4c65e1bffaee2a0311d537b261b, M = {70} 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 23:18:06 · history