Equation 677 Database

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Magma 6690ab09fb16…

magma 6690ab09fb16
Size
381
Isomorphism class hash
6690ab09fb167b519586a1e0a222ab151ce611749b6e4f20ad6367a69e9b6fbd
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 23:18:36
Display reorder
380,61,83,65,79,75,70,326,88,66,74,62,72,81,63,80,76,71,327,89,67,60,73,82,64,78,77,69,328,87,68,91,104,113,109,105,100,323,118,96,95,92,102,111,93,110,106,101,324,119,97,90,103,112,94,108,107,99,325,117,98,116,114,85,86,84,115,362,368,361,345,360,337,335,336,378,369,174,165,178,164,160,155,308,173,151,156,175,157,166,179,162,161,153,309,171,152,176,158,167,177,163,159,154,307,172,150,144,126,135,134,130,125,305,143,121,148,145,127,136,149,132,131,123,306,141,122,146,128,137,147,133,129,124,304,142,120,138,139,170,168,169,140,364,338,363,348,370,371,347,349,374,346,58,49,31,45,44,36,312,54,35,40,59,41,50,32,46,42,37,313,55,33,57,39,48,30,47,43,38,311,56,34,28,10,19,15,14,6,315,24,5,0,29,11,20,2,16,12,7,316,25,3,27,9,18,1,17,13,8,314,26,4,22,23,51,52,53,21,354,339,353,351,376,365,350,352,379,375,271,252,276,247,243,289,303,266,284,294,272,295,254,277,246,241,290,301,264,282,270,296,253,278,248,240,288,310,265,283,275,297,257,250,242,293,300,268,286,279,273,298,255,280,251,244,291,329,269,287,274,299,256,281,249,245,292,302,267,285,263,261,259,260,258,262,343,344,359,367,358,357,333,334,373,377,235,223,205,222,218,213,319,231,209,214,236,215,224,206,220,219,211,317,232,210,238,216,225,207,221,217,212,318,180,208,239,195,185,200,196,191,322,229,187,202,234,193,186,203,201,197,192,320,230,188,237,194,184,204,199,198,190,321,233,189,183,181,228,226,227,182,331,372,340,366,356,341,355,330,342,332 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#0effecc631b9063b611e8121df7e3bf991837e519c86db48be6642e79e27c755, M = {66} 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 23:18:37 · history