Equation 677 Database

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Magma 73a96641bd51…

magma 73a96641bd51
Size
381
Isomorphism class hash
73a96641bd510a46fa0e84f39e6a5728748c8f36c93b11dd00985e8ef38de611
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 23:42:32
Display reorder
380,104,99,109,114,294,119,64,69,59,54,244,49,79,83,74,284,94,89,264,269,279,249,254,259,29,34,24,44,299,39,321,322,323,318,319,320,134,124,129,149,139,144,209,199,204,194,184,189,229,219,224,289,234,239,17,16,214,18,19,274,164,159,154,174,179,169,369,334,364,344,349,338,354,379,374,359,103,98,108,113,293,118,63,68,58,53,243,48,78,82,73,283,93,88,263,268,278,248,253,258,28,33,23,43,298,38,325,326,324,328,329,327,133,123,128,148,138,143,208,198,203,193,183,188,228,218,223,288,233,238,12,13,213,15,14,273,163,158,153,173,178,168,368,333,363,343,348,339,353,378,373,358,102,97,107,112,292,117,60,65,56,51,241,46,77,81,72,282,92,87,261,266,276,245,250,255,25,31,21,40,295,36,308,306,307,311,309,310,132,122,127,147,137,142,207,197,202,192,182,187,225,216,221,286,231,236,4,3,210,0,2,271,162,157,152,172,177,167,365,332,362,342,346,335,352,376,372,355,101,95,106,110,291,115,61,66,55,52,240,47,75,84,70,281,90,85,260,265,275,246,251,256,26,30,20,41,296,35,303,304,305,301,300,302,130,121,125,145,136,141,205,195,200,191,180,186,226,215,220,285,230,235,7,1,211,5,6,270,161,156,151,170,175,165,366,330,361,341,345,336,351,375,370,356,100,96,105,111,290,116,62,67,57,50,242,45,76,80,71,280,91,86,262,267,277,247,252,257,27,32,22,42,297,37,312,313,314,315,316,317,131,120,126,146,135,140,206,196,201,190,181,185,227,217,222,287,232,237,8,11,212,9,10,272,160,155,150,171,176,166,367,331,360,340,347,337,350,377,371,357 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 = {76} 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 23:42:33 · history