Equation 677 Database

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Magma 9f089750f38d…

magma 9f089750f38d
Size
381
Isomorphism class hash
9f089750f38deb4642eb54bd296cd37f6645375ef29d6e3f2989f299091223bc
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 23:43:02
Display reorder
380,327,329,328,326,324,325,103,108,113,118,293,123,78,83,88,93,288,98,43,278,38,58,48,53,153,158,163,168,173,177,180,186,190,196,201,206,254,244,249,269,259,264,73,63,68,283,6,7,29,34,274,14,19,23,128,138,133,148,143,298,239,234,229,219,224,214,343,348,369,353,339,363,357,334,371,379,300,301,302,303,304,305,100,107,110,117,292,122,75,82,85,90,286,95,40,276,35,56,45,51,152,157,162,167,172,176,181,188,192,198,202,208,250,241,246,265,255,260,71,62,66,281,3,1,26,31,270,10,15,20,127,137,132,147,142,297,236,231,226,216,220,211,341,346,366,351,335,362,355,330,370,375,310,309,311,306,307,308,102,105,111,116,290,120,77,80,86,92,287,97,41,275,36,55,46,50,150,155,160,166,171,178,183,187,193,197,203,207,251,242,245,266,256,261,72,61,67,282,4,5,25,30,271,12,18,24,126,136,131,146,140,296,235,230,225,215,221,210,340,347,365,352,336,361,356,331,372,376,322,321,323,318,319,320,101,106,112,115,291,121,76,81,87,91,285,96,42,277,37,57,47,52,151,156,161,165,170,175,182,185,191,195,200,205,252,243,248,267,257,262,70,60,65,280,0,2,27,32,272,13,17,21,125,135,130,145,141,295,237,232,227,217,222,212,342,345,367,350,337,360,359,332,373,377,317,316,315,313,314,312,104,109,114,119,294,124,79,84,89,94,289,99,44,279,39,59,49,54,154,159,164,169,174,179,184,189,194,199,204,209,253,240,247,268,258,263,74,64,69,284,8,9,28,33,273,11,16,22,129,139,134,149,144,299,238,233,228,218,223,213,344,349,368,354,338,364,358,333,374,378 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#c3f553b30d54716d9e2e87cb9ed350bbbf2e522a2867abba1f7ef649b9b0800a, 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 23:43:03 · history