Equation 677 Database

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Magma f15e94e123a4…

magma f15e94e123a4
Size
381
Isomorphism class hash
f15e94e123a40dbe62d458f6c4c892ef821585dae884ab65f7b566969d4b2719
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 23:21:40
Display reorder
380,145,136,126,312,314,316,240,251,230,76,85,66,200,210,215,221,41,50,32,155,165,151,171,25,6,15,101,110,91,181,255,191,196,271,175,276,186,140,131,313,315,235,290,61,71,226,35,57,160,20,1,96,106,260,265,121,317,246,80,205,46,281,10,115,286,296,357,331,350,347,377,370,340,335,369,360,148,138,128,321,323,319,243,254,234,78,88,68,204,213,218,223,43,53,34,158,168,154,173,28,8,18,103,113,94,183,258,194,199,274,179,278,188,143,133,322,318,238,294,64,73,229,38,58,163,23,4,98,108,263,269,124,320,248,83,209,48,283,13,118,289,298,356,332,353,346,376,373,344,337,368,364,146,135,125,329,325,327,241,250,231,75,86,65,201,211,216,220,40,51,31,156,166,150,170,26,5,16,100,111,90,180,256,190,195,270,176,275,185,141,130,324,326,236,291,60,70,225,37,56,161,21,0,95,105,261,266,120,328,245,81,206,45,280,11,116,285,295,359,334,351,349,379,371,343,339,366,361,149,139,129,304,301,302,244,253,233,79,89,69,203,214,219,224,44,54,33,159,169,153,174,29,9,19,104,114,93,184,259,193,198,273,178,279,189,144,134,305,300,239,293,63,74,228,39,59,164,24,3,99,109,264,268,123,303,249,84,208,49,284,14,119,288,299,358,333,354,348,378,374,342,338,365,363,147,137,127,311,307,309,242,252,232,77,87,67,202,212,217,222,42,52,30,157,167,152,172,27,7,17,102,112,92,182,257,192,197,272,177,277,187,142,132,306,308,237,292,62,72,227,36,55,162,22,2,97,107,262,267,122,310,247,82,207,47,282,12,117,287,297,355,330,352,345,375,372,341,336,367,362 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#4422b92082c5ba9f603861f57ee03bc11c9f901f0082cee83e1cd8bfe00bbd4d, 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 23:21:42 · history