Equation 677 Database

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Magma d3ae65f762d7…

magma d3ae65f762d7
Size
381
Isomorphism class hash
d3ae65f762d74fe34d865bc8ccdebcbb02594b9a0f4296dd192169c989d4abbb
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 23:30:53
Display reorder
380,7,163,248,226,64,39,198,223,275,267,327,326,129,134,138,148,153,178,193,183,118,108,69,88,17,24,31,6,168,158,253,243,238,231,54,59,49,44,203,208,213,218,270,290,257,261,328,329,325,324,143,173,188,283,123,113,99,104,74,93,78,83,10,26,295,288,353,379,333,348,340,373,358,338,365,363,4,162,246,227,63,38,195,220,278,265,309,308,128,133,137,147,152,176,190,180,117,107,68,87,15,21,33,5,167,157,250,241,236,232,53,58,48,43,200,205,210,215,274,293,256,260,310,311,307,306,142,171,185,282,122,112,98,103,73,92,77,82,11,28,298,286,352,378,332,347,344,372,357,337,368,360,1,161,245,225,62,37,197,221,276,266,302,304,125,130,135,145,150,175,191,181,116,106,67,85,16,22,30,0,165,156,251,240,235,230,52,57,47,42,201,207,211,217,272,291,255,262,301,300,303,305,140,170,186,280,121,111,97,102,72,90,75,80,12,25,296,285,350,377,330,346,341,371,355,335,366,361,8,164,249,229,60,36,199,224,279,269,316,312,126,131,139,149,154,179,194,184,119,109,66,89,19,23,34,9,169,159,254,244,239,234,50,55,45,41,204,209,214,219,271,294,259,264,317,315,314,313,144,174,189,284,124,114,95,100,71,94,79,84,14,29,299,289,354,375,334,349,343,374,359,339,369,364,2,160,247,228,61,35,196,222,277,268,320,322,127,132,136,146,151,177,192,182,115,105,65,86,18,20,32,3,166,155,252,242,237,233,51,56,46,40,202,206,212,216,273,292,258,263,318,319,321,323,141,172,187,281,120,110,96,101,70,91,76,81,13,27,297,287,351,376,331,345,342,370,356,336,367,362 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#75c864f1b3b5ca4c55a580191a279ecc912d7e894cd469271a5b5b9ceed20bb0, M = {67} 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 23:30:54 · history