Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 89d850153417…

magma 89d850153417
Size
381
Isomorphism class hash
89d850153417e8569c645e7e821db272c22a36f88fb0313a24bc8bb235b42f2e
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 23:32:48
Display reorder
380,59,58,60,61,62,63,48,49,50,51,46,47,197,202,207,182,187,192,322,324,326,328,317,319,38,39,34,35,36,37,247,252,257,262,267,242,56,57,52,53,54,55,40,41,42,43,44,45,292,297,272,277,282,287,237,212,217,222,227,232,167,162,157,172,177,152,347,345,346,362,338,341,368,378,374,348,126,125,127,128,129,124,2,3,4,149,1,0,198,203,208,183,188,193,305,306,307,308,309,310,141,136,137,138,139,140,248,254,258,263,268,243,145,146,147,142,143,144,135,130,131,132,133,134,294,299,274,279,284,288,238,213,218,224,228,233,168,163,158,174,179,154,357,356,355,364,334,358,367,379,371,354,104,103,105,100,101,102,117,112,113,114,115,116,196,201,206,180,186,191,303,304,300,302,301,329,119,120,121,122,123,118,245,250,255,261,266,240,96,97,98,99,94,95,108,109,110,111,106,107,291,296,270,275,280,286,236,210,215,220,225,231,166,161,156,171,176,150,333,332,352,360,353,349,365,375,372,336,91,90,92,93,88,89,66,67,68,69,64,65,199,204,209,184,189,194,312,313,314,315,316,311,81,76,77,78,79,80,249,253,259,264,269,244,85,86,87,82,83,84,75,70,71,72,73,74,293,298,273,278,283,289,239,214,219,223,229,234,169,164,159,173,178,153,330,351,331,363,339,359,369,376,370,350,6,11,7,8,9,10,18,19,20,21,5,148,195,200,205,181,185,190,321,323,325,327,318,320,25,26,27,22,23,24,246,251,256,260,265,241,33,28,29,30,31,32,13,14,15,16,17,12,290,295,271,276,281,285,235,211,216,221,226,230,165,160,155,170,175,151,344,342,343,361,337,340,366,377,373,335 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#81fb02f374018e52eb43ccfa7482c1ceb3842f71095f08d9a76873470f8f397e, 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 23:32:49 · history