Equation 677 Database

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Magma 169940d3ac13…

magma 169940d3ac13
Size
381
Isomorphism class hash
169940d3ac13395a47d5ffb6199d5e295c3f99f0aad5eb796473bd158a514a0e
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 23:43:07
Display reorder
380,280,276,295,260,265,270,324,325,326,327,328,329,246,236,241,231,220,226,22,27,252,37,42,32,121,111,116,109,95,101,206,211,215,190,195,200,175,180,170,161,166,156,286,1,0,3,2,186,81,71,76,256,85,90,130,125,135,140,145,150,60,66,291,55,47,50,342,335,345,356,375,350,361,330,366,370,282,277,297,262,267,272,302,301,300,305,303,304,247,237,242,232,222,227,20,25,251,35,41,30,122,112,117,105,97,102,207,212,217,192,197,202,177,182,172,162,167,157,287,9,10,8,11,187,82,72,77,257,87,92,132,127,137,142,147,152,62,67,294,57,45,51,341,337,347,357,377,352,362,332,367,372,281,275,296,261,266,271,307,308,306,310,311,309,245,235,240,230,221,225,21,26,250,36,40,31,120,110,115,106,96,100,205,210,216,191,196,201,176,181,171,160,165,155,285,4,7,5,6,185,80,70,75,255,86,91,131,126,136,141,146,151,61,65,290,56,46,53,340,336,346,355,376,351,360,331,365,371,284,279,299,264,269,274,316,317,315,313,314,312,249,239,244,234,224,229,24,29,254,39,44,34,124,114,119,108,99,104,209,214,219,194,199,204,179,184,174,164,169,159,289,18,19,17,16,189,84,74,79,259,89,94,134,129,139,144,149,154,64,69,293,59,49,54,344,339,349,359,379,354,364,334,369,374,283,278,298,263,268,273,320,318,319,323,321,322,248,238,243,233,223,228,23,28,253,38,43,33,123,113,118,107,98,103,208,213,218,193,198,203,178,183,173,163,168,158,288,14,15,13,12,188,83,73,78,258,88,93,133,128,138,143,148,153,63,68,292,58,48,52,343,338,348,358,378,353,363,333,368,373 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 = {73} 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 23:43:08 · history