Equation 677 Database

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Magma d38c27e36d07…

magma d38c27e36d07
Size
381
Isomorphism class hash
d38c27e36d0729ee5475876cd2411608cbab9f5a4dd6c39644f13b39b9926ae9
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 23:22:14
Display reorder
380,164,154,144,224,204,214,254,234,244,174,184,194,324,326,327,328,264,274,284,109,119,124,134,89,99,79,9,19,4,69,44,54,59,29,64,34,74,159,149,199,209,249,239,189,169,329,259,279,114,84,94,289,14,49,294,139,219,229,179,325,269,129,104,24,299,39,345,335,363,340,350,379,331,359,369,373,160,150,140,221,201,211,250,230,240,171,181,191,317,313,314,315,260,272,282,106,115,121,131,85,95,76,6,16,0,67,40,52,57,26,62,30,72,155,145,195,206,245,235,186,165,316,255,277,110,80,90,286,11,45,291,136,216,226,176,312,265,126,100,21,297,35,347,337,361,342,353,377,332,356,366,370,162,152,142,222,202,212,252,232,242,172,182,192,323,319,320,321,262,270,281,107,117,122,132,87,97,77,7,17,2,68,42,53,58,27,63,32,73,157,147,197,207,247,237,187,167,322,256,276,112,82,92,287,12,47,292,137,217,227,177,318,267,127,102,22,298,37,346,336,362,341,351,378,330,357,368,371,161,151,141,220,200,210,251,231,241,170,180,190,303,305,301,300,261,271,280,105,116,120,130,86,96,75,5,15,1,66,41,50,55,25,60,31,71,156,146,196,205,246,236,185,166,302,258,275,111,81,91,285,10,46,290,135,215,225,175,304,266,125,101,20,295,36,348,338,360,343,352,375,333,355,365,374,163,153,143,223,203,213,253,233,243,173,183,193,306,308,309,310,263,273,283,108,118,123,133,88,98,78,8,18,3,65,43,51,56,28,61,33,70,158,148,198,208,248,238,188,168,311,257,278,113,83,93,288,13,48,293,138,218,228,178,307,268,128,103,23,296,38,349,339,364,344,354,376,334,358,367,372 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#4422b92082c5ba9f603861f57ee03bc11c9f901f0082cee83e1cd8bfe00bbd4d, M = {72} 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 23:22:15 · history