Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma ee08ea39fb9a…

magma ee08ea39fb9a
Size
381
Isomorphism class hash
ee08ea39fb9a6c82bf85ade6756301187372b5592076582e0fc014e709b38da3
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 23:39:02
Display reorder
380,125,120,131,138,143,148,56,57,217,53,54,55,227,65,66,64,67,63,208,198,203,193,183,188,222,60,61,59,58,62,309,310,311,306,307,308,173,178,168,158,163,153,48,49,50,51,52,212,257,262,252,242,247,237,271,275,266,288,298,280,71,70,292,232,68,69,337,347,352,342,363,368,357,377,333,372,127,121,132,136,141,146,30,31,215,27,28,29,225,41,42,40,38,39,206,196,201,190,180,185,221,13,37,14,15,16,316,317,315,313,314,312,171,176,166,155,160,150,19,20,18,17,26,211,256,261,251,241,245,236,272,277,267,287,297,283,1,0,291,230,2,3,336,346,350,340,361,367,355,376,331,374,129,124,133,139,144,149,104,105,219,101,102,103,229,113,114,112,115,111,209,199,204,194,184,189,224,108,109,107,106,110,323,321,322,320,318,319,174,179,169,159,164,154,96,97,98,99,100,214,259,264,254,244,249,239,274,279,269,289,299,282,119,118,294,234,116,117,339,349,354,344,364,369,359,379,334,373,126,122,130,135,140,145,4,5,216,7,8,6,226,10,9,12,43,11,205,195,200,191,181,186,220,35,36,34,32,33,300,302,301,304,305,303,170,175,165,156,161,151,21,22,23,24,25,210,255,260,250,240,246,235,270,276,265,285,296,281,47,46,290,231,44,45,335,345,351,341,360,366,356,375,330,371,128,123,134,137,142,147,80,81,218,77,78,79,228,89,90,88,87,91,207,197,202,192,182,187,223,85,86,84,82,83,324,325,326,327,328,329,172,177,167,157,162,152,72,73,74,75,76,213,258,263,253,243,248,238,273,278,268,286,295,284,95,94,293,233,92,93,338,348,353,343,362,365,358,378,332,370 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#a6a871b690da3ca50898b154241f95e49e76adc5851f18be5057763f1765447f, M = {73} 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 23:39:03 · history