Equation 677 Database

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Magma 4d53759b6ade…

magma 4d53759b6ade
Size
381
Isomorphism class hash
4d53759b6adec5ef0b054b800bbe859a2aef3225e9b8614ce5c9bd6a90294f08
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 23:41:36
Display reorder
380,273,243,123,153,183,213,144,174,204,234,264,294,6,7,8,9,10,11,16,17,12,13,14,15,168,198,228,258,288,138,122,152,182,212,242,272,316,317,312,313,314,315,1,0,2,3,4,5,259,289,139,169,199,229,295,145,175,205,235,265,23,19,20,22,21,18,340,335,357,353,365,341,337,371,366,362,293,263,143,173,203,233,128,158,188,218,248,278,103,104,105,106,107,102,112,113,108,109,110,111,161,191,221,251,281,131,142,172,202,232,262,292,324,325,326,327,328,329,97,98,99,100,101,96,250,280,130,160,190,220,279,129,159,189,219,249,119,114,117,115,118,116,331,348,347,330,370,356,346,377,361,373,284,254,134,164,194,224,137,167,197,227,257,287,29,24,25,26,27,28,42,43,44,45,46,47,154,184,214,244,274,124,135,165,195,225,255,285,322,323,318,319,320,321,31,32,33,34,35,30,245,275,125,155,185,215,286,136,166,196,226,256,41,37,38,40,39,36,350,342,351,343,367,334,352,375,369,363,283,253,133,163,193,223,149,179,209,239,269,299,73,74,75,76,77,72,61,62,63,64,65,60,156,186,216,246,276,126,132,162,192,222,252,282,306,307,308,309,310,311,81,82,83,78,79,80,247,277,127,157,187,217,298,148,178,208,238,268,68,70,71,67,66,69,336,344,338,345,368,349,359,374,360,372,297,267,147,177,207,237,141,171,201,231,261,291,94,95,90,91,92,93,51,52,53,48,49,50,150,181,211,241,271,120,146,176,206,236,266,296,300,302,303,304,305,301,88,89,84,85,86,87,240,270,121,151,180,210,290,140,170,200,230,260,58,54,55,57,56,59,332,333,354,339,379,358,355,376,364,378 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#b66edbbdcc18ab822aeb8c0e517cc0500614bfcd68d760a94b6b8cc01b086dc5, 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 23:41:37 · history