Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma ac97ef715f21…

magma ac97ef715f21
Size
381
Isomorphism class hash
ac97ef715f214649b220d79a0983fcedfbb51178ba9f4051eda8bea7799677f6
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 23:37:18
Display reorder
380,233,228,223,213,208,318,319,320,326,328,325,218,178,183,188,193,198,203,276,70,65,55,61,53,23,17,268,13,3,8,133,293,128,148,138,143,105,110,103,286,120,115,43,48,38,273,33,28,281,95,90,81,86,78,263,254,258,248,238,243,168,298,173,153,158,163,368,343,373,333,358,348,338,363,353,378,230,225,221,212,205,317,315,316,314,312,313,216,177,180,185,191,196,200,278,73,68,58,63,52,20,19,266,10,0,5,132,292,127,147,137,142,108,113,102,288,123,118,42,47,37,272,32,27,283,98,93,83,88,77,260,251,256,245,235,240,165,295,171,152,156,161,367,342,370,331,357,347,336,362,352,377,231,226,220,211,207,311,309,310,308,306,307,217,176,181,186,190,195,201,275,71,66,56,62,51,21,15,265,12,2,7,131,290,126,146,135,141,106,111,101,285,121,116,40,46,35,271,31,25,280,96,91,80,85,76,261,250,255,246,236,241,167,297,172,150,157,162,366,341,371,330,355,345,335,360,350,375,232,227,222,210,206,322,323,324,327,321,329,215,175,182,187,192,197,202,277,72,67,57,60,50,22,16,267,11,1,6,130,291,125,145,136,140,107,112,100,287,122,117,41,45,36,270,30,26,282,97,92,82,87,75,262,252,257,247,237,242,166,296,170,151,155,160,365,340,372,332,356,346,337,361,351,376,234,229,224,214,209,303,304,305,301,300,302,219,179,184,189,194,199,204,279,74,69,59,64,54,24,18,269,14,4,9,134,294,129,149,139,144,109,114,104,289,124,119,44,49,39,274,34,29,284,99,94,84,89,79,264,253,259,249,239,244,169,299,174,154,159,164,369,344,374,334,359,349,339,364,354,379 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#9acf37934a26f07a9500b1ccb24642817fa617552582595ca38f94c8a1f3c019, M = {74} 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 23:37:19 · history