Equation 677 Database

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Magma 7989dd739da4…

magma 7989dd739da4
Size
381
Isomorphism class hash
7989dd739da44135c4b8082636d092a2a58fc712fe140d0912f731dd2db40994
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 23:16:01
Display reorder
380,77,72,67,87,97,297,317,313,315,322,319,321,203,213,193,173,183,163,127,107,117,157,137,147,234,244,224,264,274,254,217,197,207,187,167,177,103,113,123,133,143,153,52,57,287,44,45,62,248,229,238,278,258,268,43,42,94,84,41,294,40,37,36,284,38,39,338,344,347,354,373,367,334,357,362,377,76,71,65,86,95,295,300,302,301,304,305,303,202,211,192,171,180,161,125,106,115,156,136,146,230,240,221,261,270,251,215,196,206,185,165,175,101,110,120,130,141,150,51,56,286,30,31,60,246,225,236,276,255,266,20,19,92,81,21,291,5,4,3,280,2,0,336,340,346,350,370,365,330,355,361,375,79,74,69,89,99,299,311,309,310,308,306,307,204,214,194,174,184,164,129,109,119,159,139,149,231,241,220,260,271,250,219,199,209,189,169,179,104,114,124,134,144,154,54,59,289,48,49,64,249,228,239,279,259,269,18,17,91,82,16,290,12,14,13,282,11,15,339,342,349,351,374,369,331,359,363,379,78,73,68,88,98,298,327,328,329,324,325,326,200,210,190,172,182,162,128,108,118,158,138,148,233,243,223,263,273,253,218,198,208,188,168,178,100,111,121,131,140,151,53,58,288,46,47,63,247,226,237,277,257,267,28,27,90,80,29,292,24,23,22,283,26,25,337,343,348,352,371,368,333,358,360,378,75,70,66,85,96,296,320,323,318,314,316,312,201,212,191,170,181,160,126,105,116,155,135,145,232,242,222,262,272,252,216,195,205,186,166,176,102,112,122,132,142,152,50,55,285,32,1,61,245,227,235,275,256,265,34,35,93,83,33,293,10,9,8,281,7,6,335,341,345,353,372,366,332,356,364,376 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#056eca7eaa44680acb1d0f30609b5545e916e9d925bf21b77056bf3e64b490d0, 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 23:16:02 · history