Equation 677 Database

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Magma e03a8268f28b…

magma e03a8268f28b
Size
381
Isomorphism class hash
e03a8268f28bad9b742af7021d3069b6d9ef0824607f8800277b9ad1ac902653
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 23:20:41
Display reorder
380,269,254,284,299,224,239,106,107,102,103,104,105,17,12,13,14,15,16,22,23,18,19,20,21,142,150,165,180,195,126,226,241,256,271,285,211,315,316,317,312,313,314,246,261,276,291,216,231,98,99,100,101,96,97,186,201,125,140,156,171,164,179,194,209,134,149,364,335,348,347,334,371,350,366,351,379,260,245,275,290,215,230,27,28,29,24,25,26,71,66,67,68,69,70,65,60,61,62,63,64,146,161,176,191,206,131,236,251,266,281,296,221,327,328,329,324,325,326,243,258,273,288,213,228,30,31,32,33,34,35,183,198,122,137,153,168,155,170,185,200,124,139,357,342,336,337,343,368,361,376,359,370,265,250,280,295,220,235,75,76,77,72,73,74,90,91,92,93,94,95,88,89,84,85,86,87,148,163,178,193,208,133,238,253,268,283,298,223,323,318,319,320,321,322,248,263,278,293,218,233,78,79,80,81,82,83,188,203,128,143,158,173,160,175,190,205,130,145,355,345,332,344,346,373,362,378,360,375,267,252,282,297,222,237,38,39,40,41,36,37,55,56,57,58,59,54,51,52,53,48,49,50,135,151,166,181,196,120,225,240,255,270,286,210,308,309,310,311,306,307,244,259,274,289,214,229,45,46,47,42,43,44,184,199,123,138,154,169,162,177,192,207,132,147,356,340,338,339,341,369,363,365,358,377,264,249,279,294,219,234,11,6,7,8,9,10,109,110,111,112,113,108,117,118,119,114,115,116,141,157,172,187,202,127,232,247,262,277,292,217,303,304,305,301,300,302,242,257,272,287,212,227,4,5,1,0,2,3,182,197,121,136,152,167,159,174,189,204,129,144,353,349,333,330,331,367,354,372,352,374 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#3136fd46544160d7110a12defb5eea5a4c1d4e69d8e8a4280fa062cfc3b165d6, M = {68} 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 23:20:42 · history