Equation 677 Database

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Magma 22e66ab4cc7c…

magma 22e66ab4cc7c
Size
381
Isomorphism class hash
22e66ab4cc7cf47e745d413e79d76d8705988f716d45c438110304c1b76f3ac3
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 23:42:49
Display reorder
380,186,196,192,211,202,207,266,271,262,250,256,245,310,311,309,307,308,306,282,42,47,37,27,32,51,285,56,60,65,71,151,140,145,136,127,133,181,170,175,166,155,161,81,290,76,95,86,91,101,295,106,112,116,122,236,231,240,215,220,225,10,20,15,276,2,9,342,350,336,355,360,375,331,370,345,367,185,198,190,213,203,208,267,272,261,251,255,246,314,312,313,317,315,316,281,40,45,36,25,31,52,287,57,62,67,72,153,143,148,138,126,130,183,173,177,168,158,163,82,292,77,97,87,92,103,298,108,110,118,120,235,230,241,216,221,226,11,21,16,275,0,5,341,352,335,358,361,377,330,374,347,368,188,197,193,210,200,205,265,270,260,252,257,247,329,327,328,326,324,325,283,43,48,38,28,33,53,288,58,63,68,73,152,142,147,137,128,132,182,172,178,167,157,162,83,293,78,98,88,93,102,297,107,113,117,123,237,232,242,217,222,227,12,22,17,277,3,6,343,354,337,357,362,378,332,372,348,366,187,195,191,212,201,206,269,274,264,254,259,249,320,318,319,323,321,322,280,41,46,35,26,30,50,286,55,61,66,70,150,141,146,135,125,131,180,171,176,165,156,160,80,291,75,96,85,90,100,296,105,111,115,121,239,234,244,219,224,229,14,24,19,279,4,8,340,351,339,356,364,376,334,371,346,365,189,199,194,214,204,209,268,273,263,253,258,248,304,305,303,300,302,301,284,44,49,39,29,34,54,289,59,64,69,74,154,144,149,139,129,134,184,174,179,169,159,164,84,294,79,99,89,94,104,299,109,114,119,124,238,233,243,218,223,228,13,23,18,278,1,7,344,353,338,359,363,379,333,373,349,369 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#c3f553b30d54716d9e2e87cb9ed350bbbf2e522a2867abba1f7ef649b9b0800a, M = {69} 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 23:42:50 · history