Equation 677 Database

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Magma 5230fa1f9aa5…

magma 5230fa1f9aa5
Size
381
Isomorphism class hash
5230fa1f9aa532af36ee2b867268e8fa3a00e63eac0aaa61d68acce290000f38
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 23:20:05
Display reorder
380,134,148,125,143,126,139,130,121,144,311,132,312,149,123,141,127,140,131,122,145,147,313,133,124,142,128,138,129,120,146,173,165,151,314,169,164,160,174,156,178,171,166,152,315,170,162,161,175,157,179,172,167,150,316,168,163,159,176,158,177,154,155,136,137,135,153,374,346,345,343,376,361,360,359,377,344,205,219,227,214,231,210,237,223,218,320,206,321,220,225,215,232,211,238,224,216,221,322,204,226,213,233,212,239,222,217,187,182,191,317,183,201,200,230,196,235,188,180,189,318,184,202,198,228,197,236,186,181,190,319,185,203,199,229,195,234,194,192,207,208,209,193,335,353,330,351,368,334,336,375,352,367,13,27,4,22,8,18,9,1,26,325,14,323,28,5,23,6,19,10,0,24,29,324,12,3,21,7,20,11,2,25,52,47,30,328,48,43,39,56,38,57,53,45,31,326,49,44,40,54,36,58,51,46,32,327,50,42,41,55,37,59,33,34,15,16,17,35,339,333,341,372,378,358,356,340,373,357,240,272,282,259,290,257,294,277,264,308,242,309,270,283,260,288,255,295,278,265,271,307,241,284,258,289,252,296,276,266,285,274,243,306,281,267,263,292,253,299,286,275,244,329,279,268,261,293,254,297,287,273,245,310,280,269,262,291,256,298,249,250,247,246,248,251,338,354,337,331,370,342,332,355,369,371,62,76,81,71,85,67,89,80,72,301,60,300,77,82,69,86,68,87,78,73,75,302,61,83,70,84,66,88,79,74,101,93,110,303,97,92,119,102,115,106,99,94,108,304,98,90,117,103,116,107,100,95,109,305,96,91,118,104,114,105,113,111,64,65,63,112,350,364,348,366,362,349,347,379,365,363 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#18fc683ad71bf835c93d962472c5b8d41f476fc340d80895a072fbcb35a73c32, 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 23:20:07 · history