Equation 677 Database

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Magma 17cdd5f4d63a…

magma 17cdd5f4d63a
Size
381
Isomorphism class hash
17cdd5f4d63ac985c04f95dd7ae8005609fde5be2a079cbd66be08f8bed324f4
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 23:32:13
Display reorder
380,53,52,48,49,50,51,266,240,245,251,256,261,59,54,55,56,57,58,180,186,191,196,201,206,236,210,215,220,226,231,165,170,176,150,155,160,326,327,328,329,324,325,44,45,46,47,42,43,280,285,291,296,270,275,64,65,60,61,62,63,66,71,67,68,69,70,331,337,347,370,365,346,336,361,355,375,11,10,6,7,8,9,269,244,248,253,258,263,22,23,18,19,20,21,184,188,193,198,203,209,239,214,218,223,228,233,169,174,179,154,159,163,310,311,306,307,308,309,13,14,15,16,17,12,284,288,293,298,273,278,26,27,28,29,24,25,35,34,30,31,32,33,335,341,344,373,368,345,339,363,359,378,90,95,91,92,93,94,267,242,247,252,257,262,72,73,74,75,76,77,182,187,192,197,202,207,237,212,217,222,227,232,167,172,177,152,157,162,320,321,322,323,318,319,0,2,3,4,5,1,282,287,292,297,272,277,79,80,81,82,83,78,85,84,86,87,88,89,334,343,350,372,367,338,349,362,356,377,129,128,130,131,126,127,268,243,249,254,259,264,132,133,134,135,136,137,183,189,194,199,204,208,238,213,219,224,229,234,168,173,178,153,158,164,315,316,317,312,313,314,123,124,125,120,121,122,283,289,294,299,274,279,139,140,141,142,143,138,145,144,146,147,148,149,333,330,354,374,369,353,332,360,357,379,41,40,36,37,38,39,265,241,246,250,255,260,118,119,114,115,116,117,181,185,190,195,200,205,235,211,216,221,225,230,166,171,175,151,156,161,301,300,302,303,304,305,109,110,111,112,113,108,281,286,290,295,271,276,99,100,101,96,97,98,106,105,107,102,103,104,351,348,342,371,366,352,340,364,358,376 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#7eadf19d7b6e5946b2d6ebbbf061273ea953f89e2819b4463bfb57d0a1e47218, M = {70} 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 23:32:13 · history